Question

dr. shepherd is studying a bacterial colony with a population of 29,600 bacteria. the colony is growing 5% per hour. how many bacteria will the colony contain in 12 hours? if necessary, round your answer to the nearest whole number.

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the growth rate as a decimal, and $t$ is the time. Here, $P=29600$, $r = 0.05$ (since 5%=0.05), and $t = 12$.

Step2: Substitute the values into the formula

$A=29600\times(1 + 0.05)^{12}$.
First, calculate $(1 + 0.05)^{12}$. Using a calculator, $(1.05)^{12}\approx1.795856$.

Step3: Calculate the final amount

$A = 29600\times1.795856\approx53157.3376$.

Step4: Round to the nearest whole number

Rounding $53157.3376$ to the nearest whole number gives $53157$.

Answer:

$53157$