Question

nate is culturing bacteria that have a growth rate of 10% per hour. if the current population is 12,800 bacteria, how many bacteria will there be in 8 hours? if necessary, round your answer to the nearest whole number. bacteria submit

Explanation:

Step1: Recall the exponential growth formula

The formula for exponential growth is $P(t) = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the growth rate (in decimal), and $t$ is the time.
Here, $P_0 = 12800$, $r = 0.10$ (since 10% = 0.10), and $t = 8$.

Step2: Substitute the values into the formula

Substitute the values into $P(t) = P_0(1 + r)^t$:
$P(8) = 12800(1 + 0.10)^8$

Step3: Calculate $(1 + 0.10)^8$

First, calculate $(1.10)^8$. Using a calculator, $(1.10)^8 \approx 2.14358881$

Step4: Multiply by the initial population

Now, multiply by 12800:
$P(8) = 12800\times2.14358881 \approx 27437.936768$

Step5: Round to the nearest whole number

Rounding 27437.936768 to the nearest whole number gives 27438.

Answer:

27438