Modeling with Exponential and Logarithmic Equations — Quiz Answers

Jacques deposited 1 dollars comma 900 into an account that earns 4 percent interest compounded semiannually. After t years, Jacques has 3 dollars comma 875 point 7 9 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

The estimated number of organisms in a population after t days is shown in the following table. t days estimated number of organisms, n 2 860 4 1 comma 250 6 1 comma 800 8 2 comma 600 10 3 comma 720 Which equation best models the situation?

A sum of money is invested at 12 percent compounded quarterly. About how long will it take for the amount of money to double? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

Claire deposited 2 dollars comma 500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had 2 dollars comma 762 point 3 5 in the account. What is the annual interest rate of the account? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

The amount of a sample remaining after t days is given by the equation cap p times t is equal to cap A times 1 half raised to the t over h power , where cap A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10 -mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?

A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation cap p times m is equal to 19 point 3 times 1 point 0 8 9 to the m th power to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?

Isabel deposits 6 dollars comma 000 into an account that earns 1 point 5 percent interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

The amount of a sample remaining after t days is given by the equation cap p times t is equal to cap A times 1 half raised to the t over h power , where cap A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60 percent of its original amount of Fermium- 257 The half-life of Fermium- 257 is about 100 days. About how old is the sample?

A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation cap p times m is equal to 19 point 3 times 1 point 0 8 9 to the m th power to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?

Claire deposited 2 dollars comma 500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had 2 dollars comma 762 point 3 5 in the account. What is the annual interest rate of the account? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

A sum of money is invested at 12 percent compounded quarterly. About how long will it take for the amount of money to double? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

The estimated number of organisms in a population after t days is shown in the following table. t days estimated number of organisms, n 2 860 4 1 comma 250 6 1 comma 800 8 2 comma 600 10 3 comma 720 Which equation best models the situation?

The amount of a sample remaining after t days is given by the equation cap p times t is equal to cap A times 1 half raised to the t over h power , where cap A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60 percent of its original amount of Fermium- 257 The half-life of Fermium- 257 is about 100 days. About how old is the sample?

Isabel deposits 6 dollars comma 000 into an account that earns 1 point 5 percent interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

The equation for the pH of a substance is pH is equal to negative log times open bracket cap h raised to the plus power close bracket , where H+ is the concentration of hydrogen ions. Which equation models the concentration of hydrogen ions open paren cap h raised to the plus power close paren of a solution whose pH is 7 point 2 ?

The amount of a sample remaining after t days is given by the equation cap p times t is equal to cap A times 1 half raised to the t over h power , where cap A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10 -mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?

Over time, the number of organisms in a population increases exponentially. The following table shows the approximate number of organisms after y years. y years number of organisms, n 1 55 2 60 3 67 4 75 The environment in which the organism lives can support at most 600 organisms. Assuming the trend continues, after how many years will the environment no longer be able to support the population?

Jacques deposited 1 dollars comma 900 into an account that earns 4 percent interest compounded semiannually. After t years, Jacques has 3 dollars comma 875 point 7 9 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years