Rewriting Exponential Functions Answers

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?

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?

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?

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?

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?

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?

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?

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 ?

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?

Which of the following is equivalent to ?