Rewriting Exponential Functions

The value y of an investment x months after the money was invested is given according to the equation below. y = 25,000(1.16)^-x As time goes on, does the value of the investment grow or decay?

decay

Which expression relates h, the number of half-lives, and y, the number of years?

h=y/2.6

What is the base of the exponential function?

0.86

How many grams of fermium will remain after twenty-three days?

1.986 g

Use what you know about negative exponents to choose the equation below that is equivalent.

2nd option

Find the frequency for the pitch E shown

659 Hz

Choose all equivalent expression(s). ab^-3x

C. a(1/b)^3x D. a((1/b)^3)^x

Which of the following functions represent exponential decay?

B,C,D

Fermium-253 has a half-life of three days. A sample contains 400 g. How long will it take for the sample to decay to 100 g?

Number of half-lives: 2 Number of days: 6 How many grams of fermium will remain after fifteen days? 12.5

The half-life of sodium-22 is 2.6 years. A sample contains 800 mg of this isotope. Which expression represents the mass of sodium remaining after h half-lives?

S = 800(0.5)^h

Combine the first two equations and laws of exponents to find the equation for the mass of sodium remaining after y years.

S = 800(0.766)^y

Here is the function for the number of zombies, N, after t years, with the negative exponent expressed using the fraction ½: N(t) = 300 • 0.5t/8 What is the half-life for the zombie population? Explain in terms of exponents. (To type an exponent, use the ^ key.)

Sample Answer: Eight years. To get ½ of the 300, you need 0.5^(t/8) to equal ½, or 0.5. That means that the exponent must be 1. This happens when t = 8 years. Check all facts you included in your answer. -The exponential part of the expression needs to be equal to ½, or 0.5. -The half-life time will occur at the value of t that gives an exponent of 1. -The value t = 8 causes the exponent to be 1, so that's the half-life.

Click here to listen to a keyboard play the notes starting at A and ending at E. Each note is a half-step above the previous note. How many half-steps are there between A440 and the E above it?

7

Approximately how many milligrams of sodium remain after 8.4 years?

85.2 mg

Which of the following functions represent exponential growth?

A,B,C

What formula(s) below represents the frequency of that E? Check all that apply.

A,C,E

Abel and Zöe's grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011. Abel: y = 1266.77(1.03)t Zöe: y = 1159.27(1.03)t Based upon this information, find the difference in the children's ages. Suggestions: Find the ratio 1266.77/1159.26. What does that ratio represent in terms of powers of 1.03? You also can graph both equations and figure out the shift.

Abel is 3 years older than Zöe.

Choose all equivalent expression(s).

B. (4)^-3x^2 C.(1.4)^3x^2

In the previous video, you compared the two functions below. f(x)=1.2^t g(x)=1.2^t-5

B. It shifts the graph of f right 5 units. F. It divides all the y-values by 1.25.

What formula would you use to calculate the mass of fermium-253 remaining after d days?

B. f(d)=400(0.794)^d

Sofia takes 10mg of a medicine whose concentration in blood decreases by a factor of one half every day. Let t be the number of days since Sofia took the medication. The amount of medication in her system after t days is S = 10(½)t. Four days later, Lexi takes 10mg of the same medicine. How much medication, L, is in Lexi's system on day t?

C. L=10(1/2)^t-4

Martin deposits $200 in a savings account that earns 5% annual interest. Four years later, Cary deposits $200 in an account earning the same interest. Let M represent the balance in Martin's account and let C represent the amount of money in Cary's account. Choose the pair of expressions that describe the accounts y years after Martin opened his account.

D. Martin:200(1.05)^y Cary: 200(1.05)^y-4

Which equation below compares the amount of medicine, S, in Sofia's system with the amount of medicine, L, in Lexi's system?

L=16xS

Choose the equation that relates the balances in the accounts y years after Martin opened his account.

M = 1.22C

he function below represents the number of zombies, N, where t is the number of years since the zombies gained control of Earth: N(t) = 300 · 2-t/8 Is this exponential growth or decay? Explain using your understanding of the properties of exponents. (To type exponents, use the ^ key.)

Sample Answer: This is decay. The exponent has a negative sign. The reciprocal of 2 is 0.5. So N(t) can be rewritten as 0.5^(t/8). The base is fraction less than 1, which is decay. Check all facts you included in your answer. -The negative exponent means that you must take the reciprocal of the base 2. -The reciprocal of 2 is 0.5 (or ½). -The base 0.5 (or ½) is less than 1. -Bases less than 1 cause decay.