nate is culturing bacteria that have a growth rate of 10% per hour. if the current population is 12,800…

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

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

Answer

Explanation:

Step1: Identify the growth - formula

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.

Step2: Convert the growth rate to a decimal

The growth rate $r = 10%=0.1$. The initial population $P = 12800$ and the time $t = 8$ hours.

Step3: Substitute the values into the formula

$A=12800\times(1 + 0.1)^8$. First, calculate $(1 + 0.1)^8=1.1^8$. $1.1^8=2.14358881$. Then, $A = 12800\times2.14358881$. $A=12800\times2.14358881 = 27437.936768$.

Step4: Round the answer

Rounding $27437.936768$ to the nearest whole number gives $27438$.

Answer:

$27438$