Rewriting Exponential Functions Answers

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?

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?

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 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?

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?

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 ?

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 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?

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?