Question

question 10 - 1 point
a sample of bacteria is growing at an hourly rate of 5% according to the continuous exponential growth function. the sample began with 7 bacteria.
how many bacteria will be in the sample after 20 hours? round your answer down to the nearest whole number.
provide your answer below:

Explanation:

Step1: Recall the continuous - growth formula

The continuous - exponential growth formula is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the growth rate, and $t$ is the time.

Step2: Identify the values of $P$, $r$, and $t$

Given that $P = 7$ (initial number of bacteria), $r=0.05$ (5% growth rate written as a decimal), and $t = 20$ (number of hours).

Step3: Substitute the values into the formula

$A=7e^{0.05\times20}$.

Step4: Calculate the exponent

First, calculate $0.05\times20 = 1$. So, $A = 7e^{1}$.

Step5: Evaluate the expression

Since $e\approx2.71828$, then $A = 7\times2.71828\approx19.02796$.

Step6: Round down

Rounding down $19.02796$ to the nearest whole number gives $19$.

Answer:

19