1) The population of Bloomington, Illinois grew from \(52,655\) in \(1990\) to \(78,730\) in \(2014\). Calculate the average yearly rate of change.
2) A Honda CR-V was purchased new \(\$25,750\) in \(2007\). In \(2017\), it is worth \(\$9,290\). What is the rate of depreciation for the Honda CR-V?
3) Lisle’s population decreased from \(41,244\) in \(2005\) to \(27,863\) in \(2015\). Find the average yearly rate of decline. Predict the population in \(2023\) if the rate of decrease continues.
4) The population of New York increased from \(8.2\) million in \(2010\) to \(8.5\) million in \(2016\). Find the average annual rate of increase. Next, predict the population of New York in \(2020\) if the rate of increase continues.
5) A \(2017\) Ford Escape, a compact sports utility vehicle, costs \(\$22,900\). If the Escape depreciates in value each year by \(9.6\%\), what is the Escape value after \(10\) years? Round answer the nearest cent.
6) A population of bacteria doubles every \(3\) hours. If the initial population has \(18\) colonies, how many colonies should you observe after \(14\) hours?
7) Suppose a radioactive substance decays at a rate of \(3.5\%\) per hour. What percent of substance will be left after \(6\) hours?
8) The number of bacteria in a certain culture doubles every half hour. If there were \(30\) bacteria present in the culture initially, how many bacteria will be present at the end \(8\) hours?
9) A hospital prepares a \(10\)mL supply of technetium-99m which has a half-life of \(6\) hours. Find the amount of technetium-99m that remains after \(20\) hours. Round answer to the nearest hundredth of a mL.
10) The half life of ibuprofen is about \(2\) hours. How many milligrams of ibuprofen will be left in the body after \(7\) hours if a \(200\) milligram tablet was taken? Round answer to the nearest tenth of a mg.
11) Carbon stops being absorbed into an organism when it dies. The amount of Carbon-14 in the organism then decays with a half life of \(5730\) years. If bone fossil of a mastodon is found with \(13\%\) of the Carbon-14 when it died, how old was the mastodon when the bone was found? Round answer to the nearest year.
12) You invest \(\$2500\) in bank which pays \(4.25\%\) interest per year compounded continuously. What will be the value of the investment after \(10\) years? Round answer to the nearest cent.
13) You invest \(\$500\) in a CD which pays \(3.85\%\) interest compounded quarterly. What will be the value of the investment after \(5\) years? Round answer to the nearest cent.
14) You invest \(\$700\) in a bond which pays \(3.25\%\) interest compounded monthly. When will your investment double? When your investment triple? Round answer to the nearest tenth of a year.
15) You have a balance of \(\$2325\) on a credit card. The interest rate for the credit card is \(20.99\%\) compounded daily. What will the balance of your credit card be in \(60\) days? Round answer to the nearest cent.
16) Which is the better investment option? Option A: \(3.75\%\) compounded daily. Option B: \(3.70\%\) compounded continuously. Option C: \(3.80\%\) compounded weekly. Justify your reasoning.
17) Which is the better investment option? Option A: \(4.96\%\) compounded monthly. Option B: \(4.95\%\) compounded continuously. Option C: \(4.99\%\) compounded semiannually. Justify your reasoning.
18) You have the option to refinance your credit card debt. Currently you have a balance of \(\$3700\) at \(17.99\%\) interest compounded daily. You are looking to refinance at a lower interest rate compounded daily. What interest rate will save you \(\$30\) in one month?
Review
19) Graph the function, \(f(x) = 7^{(x-2)} + 4\) and state the domain, range and horizontal asymptote.
20) If \(\Large\frac{a}{b} = \normalsize2\), what is the value of \(\Large\frac{4b}{a}\)?
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