Rewriting Exponential Functions

Nolan begins a savings account with $100 at 2% interest according to the equation mc017-1.jpg, where Vn is the value of his account after x years. Anias invests $100 at 2% interest three years after Nolan. The value of Anias's account, Va is determined using the equation mc017-2.jpg. If Anias would have invested when Nolan first invested, approximately how much money would she have needed to invest to have the same amount of money that she has three years later?

$94.23

The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation mc008-1.jpg. What is the daily percent of decrease?

12.94%

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 mc022-1.jpg. What is the annual rate of decay?

13%

The formula for determining the frequency, f, of a note on a piano is mc016-1.jpg, where h is the number of half-steps from the A above middle C on the keyboard. A note is six half-steps away from the A above middle C. The frequency of the A above middle C is 440 Hz. How much greater is the frequency of the new note compared with the frequency of the A above middle C?

41.4%

Karey is prescribed 600 mg of a medication that decays at a rate of 40% per day, d, according to the equation mc020-1.jpg, 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?

7.8%

A business owner opens one store in town A. The equation mc024-1.jpgrepresents 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?

96%

Which is an equivalent form of the expression 1800(1.2)-t?

B

Which of the following is equivalent to mc004-1.jpg? (1/2)^-2t

C

A biologist begins working with a sample containing 20,000 bacteria. The population size doubles every 10 days according to the equation mc006-1.jpg, where t represents the number of days. After seven days the biologist begins working with a second sample of 20,000 bacteria. The equation used to represent the population of sample 2 after t days is mc006-2.jpg. Which of the following is an equivalent form of the equation for the population of sample 2?

D

On a piano, the formula to determine the frequency, f, for the G above A440 is f=440*2^10/2. Which of the following is equivalent to f?

D

On a piano, the formula to determine the frequency, f, for the G above A440 is mc010-1.jpg. Which of the following is equivalent to f?

D

A radioactive element has a half-life of six days. What is the approximate decay rate of the element after the first day?

NOT 8.3%

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation mc026-1.jpg. After three days, the scientist receives a second shipment of 100 milligrams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is mc026-2.jpg. After any time, t, the mass of the element remaining in shipment 1 is what percentage of the mass of the element remaining in shipment 2?

NOT 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 mc013-1.jpg. 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 mc013-2.jpg. Which of the following is an equivalent form of the expression for the amount remaining in shipment 2?

NOT A

The population, p, of a town after t years is represented using the equation mc005-1.jpg. Which of the following is an equivalent expression?

NOT A

Consider the expression 0.8^x-3 Which of the following is an equivalent expression?

NOT B

Jana is prescribed 250 mg of medication. Seventy-five percent of the medication remains in her body after each hour, h, according to the equation mc019-1.jpg. Six hours later, Allison is prescribed the same medication. The medication remains in Allison's body according to the equation mc019-2.jpg. At any time after she has taken the medication, Allison has how many times more milligrams of medication in her body?

NOT B

An antibiotic kills 60% of bacteria in a sample of 100,000 each day. The equation mc009-1.jpgrepresents 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 mc009-2.jpg. Which equation is equivalent to p2?

NOT B NOT C

Juana invests $1,500 in an account accumulating 3% interest according to the equation mc025-1.jpg, 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?

NOT B NOT A NOT C

Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the equation mc012-1.jpg, 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?

NOT C

The value, V, of Kalani's stock investments over a time period, x, can be determined using the equation V=750(0.80)^x What is the rate of increase or decrease associated with this account?

NOT C 25%

Consider the expression 1.1(1.3)^x+4mc003-1.jpg. Which of the following is an equivalent expression?

NOT C NOT B NOT A