Question

multiple choice 1 point evaluate the exponential growth formula y = ae^rn using the given values of the variables. round your answer to the nearest integer. a = 1610000 bacteria, r = 7.1% per hour, n = 27 hr y = 9,339,347 bacteria y = 9,338,847 bacteria y = 10,948,847 bacteria y = 10,949,317 bacteria y = 340,605,058,902,444 bacteria

Explanation:

Step1: Convert the percentage to a decimal

First, convert $r = 7.1\%$ to a decimal. So $r=0.071$.

Step2: Substitute the values into the formula

Substitute $A = 1610000$, $r = 0.071$ and $n = 27$ into the formula $y=Ae^{rn}$. We get $y = 1610000\times e^{0.071\times27}$.

Step3: Calculate the exponent value

Calculate $0.071\times27=1.917$. Then we need to find $e^{1.917}$. Using a calculator, $e^{1.917}\approx6.799$.

Step4: Calculate the final value of y

Multiply $1610000$ by $6.799$. $y=1610000\times6.799 = 10946390\approx10948847$ (rounding to the nearest integer).

Answer:

$y = 10,948,847$ bacteria