Modeling with Exponential and Logarithmic Equations — Test Answers

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?

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?

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?

Juana invests $1,500 in an account accumulating 3% interest according to the equation , where v represents the value of the account after y years. Marquez and Calvin invest the same amount of money at the same rate. Marquez invests three years before Juana, and Calvin invests two years after Juana. By what factor would Calvin’s investment need to be increased to equal Marquez’s investment at any time after Calvin’s investment is made?

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?

The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation . What is the daily percent of decrease?

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

Which of the following is equivalent to ?

Nolan began a savings account three years ago. He invested $100 at a 2% interest rate according to the equation Vn = 100(1.02)x, where Vn is the value of his account after x years. Anias started an account today. She invested $100 at a 2% interest rate according to the equation Va = 100(1.02)x–3, where Va is the value of her account. Let’s say Anias started saving at the same time Nolan did, three years ago. Approximately how much money would she have had to invest to have the same amount of money she has now?