Rewriting Exponential Functions Answers

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?

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

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 ?

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?

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 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?

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?

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 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?