exponential applications

The function y = 4x is an exponential growth function. The graph of the function increases as x increases. The variable x is a(n)

exponent

(half right) In the exponential growth function y = 235(1.15)x, what is the 1. growth factor? a0 2. percent increase? a1

0.15 15

Consider the function y = 1.05(x/12), which represents the growth of capital in a bank account. The annual interest is %, and the bank compounds the interest . The balance of the account will grow

1.05 monthly exponentially

If a set has 1,024 subsets, how many elements does it have?

10

How many bicycle license tags can you make with four numeral spaces? Use 10 digits and no blank spaces.

10,000

How many cubic feet are in one cubic yard?

27

A deposit of $5,000 is made into a savings account that offers 7.5% annual interest. Which equation models the amount of money in the account after t years?

P(t) = 5,000(1.075)^t

A radioactive element decays exponentially at a rate of 0.13% each hour. Which of the following is true?

The amount of the element will decrease closer and closer to zero as time goes on.

Select all the correct statements. A community college enrolled 96,000 students in 2007, and the enrollment has increased by 7% every year since then. Graph the exponential function, y, that gives the number of students enrolled in terms of t, where t is the number of years since 2007.

The graph of the function begins at y = 96,000. The graph of the function shows the exponential growth

The initial count of a certain type of bacteria in a culture is 350. If the bacteria grows at the rate of 20% per hour, which function models the number of bacteria after t hours?

f(t) = 350e^12t

(half right) Select all the correct statements. Which of the following are examples of exponential growth functions?

y = 5(1.01)^t y = 0.25e^-1.1t y = 11(1 - 0.0001)^4t y = 3e^0.00001t y = 1,000(0.23)^-1.2t

Solve the following application problem. The Farm Agency can use the letters A, B, C, and blank spaces to make tags. Let y be the number of tags they can make using n spaces. What is the formula for the number of tags they can make?

y=3^n

A loaf of bread is removed from an oven and is left sitting in the kitchen to cool. Its temperature t minutes after being removed from the oven is given by the equation T(t) = 103e-0.0182t + 73. Find the temperature of the kitchen (assuming the temperature remains constant), the initial temperature of the bread when it is removed from the oven, and the temperature of the loaf of bread after 90 minutes. Temperature of the kitchen: a0 Initial temperature of the loaf of bread: a1 Temperature of the loaf of bread after 90 minutes (rounded to the nearest whole degree):

73 176 93

A warm object cools according to the function T(t) = 249e^-0.035t + 82. Assuming a constant environmental temperature, what constant temperature, in °F, will the object's temperature eventually stabilize?

82°F

If $1,100 is deposited into a savings account offering 11% interest paid annually, approximately how much money will be in the account in 10 years?

$3,123

Jason made a payment of $1800 to his bank to clear his debts. He then deposited $1000 in his checking account at an annual interest rate of 6% compounded monthly. Jason made the following graph to relate the amount accumulated in his checking account in x number of years. What is the domain of the graph that Jason plotted?

[0, ∞)

If a set has three elements, how many subsets does it have?

8

The volume of a cubical bin is 27 cubic feet. What are its length, width, and height? Which of the following equations could represent the word problem given?

27=x^3

A car is purchased for $20,000. In two years, the car is valued at $18,050. What is the rate of depreciation of the car?

5%

If an agency needs to make 1,000,000 tags, how many numeral spaces should they use? Use 10 digits and no blank spaces.

6

The formula for the nth term b of a geometric series is b=ar^n-1. Find n when b=1,024, a=16 and r=2.

7

The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?

7%

Elaine deposited $500 at 4.25% compounded continuously for t number of years. Model the given situation with a function showing the amount A, accumulated after t years. Find the domain of the function.

A= 500* (1+ 4.25/100)^t Domain: (-infinity, infinity)

A lake has the capacity to support 10,000 trout. Suppose that the conditions are such that the current population of trout will grow logistically up until it stabilizes at the amount that the lake can support. Currently there are 1,500 trout in the lake. Which of the following is a possible model for P(t), the trout population in t years?

P(t)=10,000/1+9e^-0.48t

A population of endangered birds decreases by 3% each year. If the current population is 30,000 birds, write an equation that represents the number of birds, N, in terms of the number of years, T, from the present. Approximately what will the bird population be after twenty years? Round your answer to the nearest thousand.

a) The required equation is, N= 30,000(0.97)^t b) The approximate population of the birds after 20 years is 16,314.

Solve the following application problem. The Farm Agency is to use only the letters A, B, and C to make tags. Let y be the number of tags they can make using n spaces. What is the formula for the number of tags they can make?

y=3^n