algebra 1b - unit 2: more about functions by:Lily_Malik5

according to the experts, about how much should the baseball card be worth in 30 years?

$15,540.35

using this equation, what would the company's approximate annual income be in the year 2009?

$258,000

you plan to invest $350 in a growth fund that has a rate of 1.5% compounded quarterly. how much money will this investment be worth after 50 years?

$739.91

which table of values represents the exponential function f(x) = 0.1^x - 4?

-1, 6 ......

volunteers recently planted a new tree in the town square, and its leaves are doubling in number each month. this will last for only 3 more months, until the end of summer. if the tree began with 246 leaves, how many leaves will it have before autumn?

1,968

what is the approximate new interest rate?

9.6%

which statement is true about the graphs?

both graphs have the same horizontal asymptotes.

which of the following equations is a function that will predict c(h), the number of cells after h hours have passed?

c(h) = 120(2)^h

which function has a horizontal asymptote equal to 2?

f(x) = 4 * 3^x + 2

a linear function is represented by the values in the following input-output table. what is the rate of change of the function?

-1/2

james is contemplating an investment opportunity represented by the function a(t) = p(1.06)^t, where p is the initial amount of the investment, and t is the time in years. if james invests $5000, what is the average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20?

811

which recursive formula represents the sequence {1, 2, 4, 8, 16,...}?

a1 = 1, and an = 2a (n - 1)

what is the first term of the sequence, and what is the recursive rule that describes the sequence?

a1 = 6,561; an = 1/3 a(n - 1)

a value in a sequence is 2 times the previous value, like this: {8, 16, 32, 64}. how would this sequence be represented as a recursive equation?

a1 = 8 and an = 2a(n-1)

use the following partial table of values of a geometric sequence to answer the question. which function rule could represent this sequence?

f(n) = 0.0625(4)^n-1

checkpoint: use the following partial table of values of a geometric sequence to answer the question. which function rule could represent this sequence?

f(n) = 2(2)^n-1, where n is a natural number

what is the explicit formula, in function notation, that could produce the sequence?

f(n) = 4(1/2)^n-1

which function represents the amount of money in the account after t years?

f(t) = 1,000(1.12)^t

which function represents the value of the car after t years?

f(t) = 21,000(0.85)^t

which of these is another way to write the function f(x) = 5^x?

f(x) = (625^x)^1/4

which function will have a graph that decreases?

f(x) = 1.25 * 0.3^x + 7

lesson 6

geometric sequences

lesson 8

growth vs. decay

which function has the greatest growth factor?

j(t)

lesson 10

rate of change

which answer represents a geometric sequence?

{1, 3, 9, 27, ...}

which answers are geometric sequences? select all that apply.

{2, -10, 50, -250, ...} {108, 36, 12, 4, ....} {1, -1, 1, -1, 1, ....}

checkpoint: which answer represents a geometric sequence?

{−1008, −504, −252, −126,...}

if the interest is compounded monthly, what will the approximate balance of this savings account be after 3 years?

$8,842

what is the rocket's average rate of change from 3 ≤ t ≤ 6 in yards/second?

-11

which table of values represents the exponential function f(x) = (1/5)^x?

-2, 25......

what is the horizontal asymptote of the function f(x) = 2^x - 5?

-5

what is the average rate of change of the car's value in dollars per year (rounded to the nearest dollar) during the first 4 years kenzie owns it?

-660

james deposited some money into a savings account to save for a motorcycle. based on the interest rate of the account, he estimates that his money will grow according to the following table. the values follow a geometric sequence. what is the common ratio of the sequence?

1.02

how much money would you have after 10, 20 and 30 years?

10 years: $1,552.92 20 years: $4,823.15 30 years: $14,979.96

nick recently started a landscaping company. he began with 3 clients. thanks to word-of-mouth referrals, his clients double each month. how many clients will nick have after one year?

12288

about how much money is the car worth after the second year?

14,100.03

approximately how much money would be in your account after the third year?

1404.93

what will the approximate population of bald eagles be in the year 2030?

1518

what is the rate of change for the linear function that contains the points (−3, 2) and (1, 10)?

2

if x represents the number of years since its prime, what was the rock band's tour attendance in 1990?

26.4 million

what is the average rate of change over the interval 1 ≤ x ≤ 3?

3

suppose you borrow $500 and you plan to pay it back all at once in 5 years. you are charged 2% interest compounded monthly. what is the total amount you will need to pay when the loan is due?

553

an ancient artifact was recently discovered, but due to rust and corrosion, only 75 grams of the original item remained. based on historical dates, scientists believe that this artifact was decaying at a rate of 2% each year. although the artifact will now be preserved at a museum, scientists wonder: how much of the original artifact would there be if they had not discovered it for another 10 years? write an exponential function rule and solve.

61

if the number of bacteria on the surface of your phone triples every hour and can be described with the exponential function f(x)= 1,000 * 3x, complete the blank in the table of values to show how much bacteria is on your phone after 4 hours.

81000

which of the following functions is equivalent to the function below? select three that apply. f(x) = (1/3)^2x

9^-x 3^-2x (1/9)^x

which equation shows how jane can rewrite the formula to find the annual percentage rate that would cost her the same amount if it compounded semi-annually?

a = 1500(1.095)^2t

which answer shows how the equation can be rewritten to find the interest rate that would cost bill's company the same amount if it were compounded quarterly?

a = 2500(1.0799)^4t apr = 31.96%

in order for the loan at bank b to cost the swim school the same amount, what apr would bank b need to offer?

a = 55,000(1.118)^2t apr = 23.6%

which statement describes a geometric sequence?

a sequence of numbers in which each term is produced by multiplying the previous term by a common ratio

the popularity of a new music artist has been growing exponentially each week. the table shows how many song downloads the artist has had so far. which of the following is a recursive formula that represents the information in the table?

a1 = 75 and an = a(n - 1) * 6

which of the following statements is supported by the behavior of c(t)?

according to c(t), the concentration of organisms will increase over time.

which option can be modeled by a linear function?

adding $2 to a piggy bank each week.

which statements are true for calculating the common ratio, r, based on the table of values?

all that equal 14

consider the following graph of an exponential function modeling the geometric sequence 1, 3, 9, 27... which of the following statements are valid based on the graph?

all that equal 3

which statements show that the function grows by equal factors, where rr represents the growth rate?

all that equal 7

study the geometric sequence {−4, −84, −1764, −37044,...}. what is the explicit formula for the sequence?

an = (-4)(21)^(n-1)

a geometric sequence has a common ratio of 2 and the 12th term is −12,288. what is the explicit rule that describes this sequence?

an = -6 * 2^(n - 1)

what is the explicit rule that describes the sequence?

an = 0.3(0.1)^(n - 1)

the common ratio of a sequence is 3. two terms in the sequence are a4 = 3 and a8 = 243 what is the explicit rule that describes this sequence?

an = 1/9(3)^n-1

two values of a geometric sequence are a2 = 33 and a3 = 363. what is the explicit formula for this sequence?

an = 3 * 11^(n - 1)

consider the terms in the sequence: {1/3, 1/9, 1/27, ....} match each expression with the correct answer.

common ratio of the sequence: r = 1/3 first term in the sequence: a1 = 1/3 recursive rule that describes the sequence: an = 1/3 an - 1

match each expression with the correct answer.

common ratio of the sequence: r = 8 first term in the sequence: a1 = 4 recursive rule in function notation that describes the sequence: f(n) = 8f(n - 1)

what is the rate of change of the graphed function?

every year, the height increases by 5 inches, so the rate of change is 5 inches/year

lesson 7

exponential functions

is this situation an example of exponential growth or exponential decay?

exponential growth

which expression is equivalent to f(x) = 8^-x / 8^y?

f(x) = 1/2....

which function represents the fish population after x years?

f(x) = 10,000(1.5)^x

hot tea is around 181 degrees fahrenheit, and the room temperature is 72 degrees fahrenheit. the rate of the hot tea cooling on a desk in the room is about 6.5% every minute. you need to determine how hot the tea will be after t minutes? which function models this situation?

f(x) = 109(0.935)^t + 72

which exponential function rule represents kayla's business?

f(x) = 43 * 1.035^x

compare the following functions f(x) and g(x). which function increases at the fastest rate?

f(x) increases at a faster rate

the common ratio of a sequence is 1/2.... match each expression with the correct answer.

first term in the sequence: a1 = 16 recursive rule that describes the sequence: an = 1/2 an - 1

compare the following exponential functions: f(x), g(x), and h(x). which function increases at the fastest rate?

g(x)

which function increases at the fastest rate?

g(x)

which of these is another way to write the function g(x) = 3^x?

g(x) = 9(3^x-2)

which answers show another way to write the function g(x) = 27^x? select all that apply.

g(x) = 9^x * 3^x g(x) = 3^3x g(x) = 3^2x * 3^x g(x) = (1/27^-x)

which statements about geometric sequences are true? select all that apply

geometric sequences are restricted to the domain of natural numbers. geometric sequences have a common ratio between terms.

which explanation correctly addresses juan's assumption?

he is correct. the tea will cool exponentially since it cools at a percentage rate every minute.

how does the exponential function f(x) = 2 ⋅ 3^x + 4 appear as a graph?

https://cdstools.flipswitch.com/asset/media/1042439

which answer shows the graph of the function f(x) = 2 * 0.5^x - 5?

https://cdstools.flipswitch.com/asset/media/1155269

sketch the graph of the exponential function f(x) = 3^x - 3. which graph is the correct representation of the function?

https://cdstools.flipswitch.com/asset/media/1155280

suppose you want to write an expression in the form a(b^c) to represent the area of the wound in square millimeters n days after it began to heal. which of these statements are correct? select two that apply.

if the value of c is n, the value of a is 31.25 if the value of c is n, the value of b is 0.8.

1. which statements about the functions are true?

over the interval −8 ≤ x ≤ −3, the average rate of change of g(x) is slower than the average rate of change of f(x). over the interval 4 ≤ x ≤ 6, the average rate of change of g(x) is slower than the average rate of change of f(x). over the interval −8 ≤ x ≤ −7, the average rate of change of g(x) is slower than the average rate of change of f(x).

2. which statements about the functions are true?

the average rate of change for g(x) over the interval −1 to 0 is −3. the average rate of change for f(x) over the interval −1 to 0 is −4. the average rate of change for g(x) over the interval −2 to −1 is faster than the average rate of change for f(x). the average rate of change for f(x) over the interval 2 to 3 is faster than the average rate of change for g(x).

4. which statement about the functions is true?

the average rate of change of f(x) is faster than the average rate of change of g(x) from −3 to −2.

3. which statements about the functions are true?

the average rate of change of g(x) is faster than the average rate of change of f(x) from −2 to 0. the average rate of change of f(x) is faster than the average rate of change of g(x) over the interval 1 ≤ x ≤ 6.

suppose that f is an exponential function such that f(x) = 4 * 2^x. which answer shows that this exponential function grows by equal factors over equal intervals?

the division one

7.3-4 which function increases at a faster rate?

the function f(x) increases at a faster rate.

which of the following statements describes the value of painting a relative to the value of painting b over the next five years?

the value of painting a grows by a larger constant percent rate per year than painting b.

what is the difference between the horizontal asymptotes in graph a and graph b?

they have a difference of 5 units

lesson 9

variables in exponents