Rewriting Exponential Functions Answers

Leela invests $500 at 4.5% interest according to the equation , where Vl is the value of the account after t years. Adele invests the same amount of money at the same interest rate, but begins investing two years earlier according to the equation . The total value of Adele’s account is approximately what percent of the total value of Leela’s account at any time, t?

A business owner opens one store in town A. The equation represents the anticipated profit after t years. The business owner opens a store in town B six months later and predicts the profit from that store to increase at the same rate. Assume that the initial profit from the store in town B is the same as the initial profit from the store in town A. At any time after both stores have opened, how does the profit from the store in town B compare with the profit from the store in town A?

A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation . After two days the scientist receives a second shipment of 50 grams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is . Which of the following is an equivalent form of the expression for the amount remaining in shipment 2?

Karey is prescribed 600 mg of a medication that decays at a rate of 40% per day, d, according to the equation , where m is the amount of medication remaining in his body. Noelle takes the same medication five days earlier. The number of milligrams of medication in Noelle’s body is about what percentage of the number of milligrams in Karey’s body at any time after they have both taken the medication?

The function gives the mass, m, of a radioactive substance remaining after h half-lives. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

Which of the following is equivalent to ?

The function gives the mass, m, of a radioactive substance remaining after h half-lives. Iron has a half-life of 2.7 years. Which equation gives the mass of a 200 mg Iron sample remaining after y years, and approximately how many milligrams remain after 12 years?

Jenny invests $2,000 at an interest rate of 5%. The amount of money, , in Jenny’s account after t years can be represented using the equation . If Jenny would have invested the same amount of money at the same interest rate four years ago, the equation representing the amount of money, , in her account would be represented using the equation . Which of the following is equivalent to ?

The value, V, of Kalani’s stock investments over a time period, x, can be determined using the equation . What is the rate of increase or decrease associated with this account?

On a piano, the formula to determine the frequency of any pitch relative to the A above middle C (A440) is given by the expression , where x represents the the number of half-steps above or below A440. Which of the following is equivalent to ?

Consider the expression . Which of the following is an equivalent expression?

An antibiotic kills 60% of bacteria in a sample of 100,000 each day. The equation represents the population, p1, after d days. Four days after introducing the antibiotic to the first sample, a scientist introduces the same antibiotic to a second population, p2. The number of bacteria after d days in the second population is represented by the equation . Which equation is equivalent to p2?

Jillana takes a single dose of medication that remains in her body according to the equation r = 200(0.75)d, where r represents the amount of medication remaining after d days. If Jillana had taken the medication four days earlier, the amount of medication remaining in her system relative to the amount that remains in her system after d days would be represented using the equation r2 = 200(0.75)d + 4. Which of the following is an equivalent equation?

The half-life of a radioactive element is five years. A scientist has 18 grams of the element. The equation representing the number of grams, g, after x years is . What is the annual rate of decay?

Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the equation , where Vh is the value of the account after t years. Andres begins a savings account three years later with the same initial amount of money at the same interest rate. Which equations represent the value of Andres’s account after t years?