Question

There are 1,157 bacteria 3 days after the bacteria were introduced to the petri dish. The population is decreasing at a rate of 12% per day.(a) Determine the initial number of bacteria that were introduced to the petri dish.(b) Define a function that models the population P of bacteria in terms of the time t sincethe bacteria were introduced to the petri dish.(c) How many bacteria will there be after 10 days?

Answer 1

ANSWER:

(a) 1698 bacterias

(b)

$P=1698\cdot(0.88)^t$

(c) 473 bacterias

STEP-BY-STEP EXPLANATION:

(a)

We can propose the following equation of the statement to calculate the initial number of bacteria, just like this:

$\begin{gathered} 1157=I\cdot(1-0.12)^3 \\ \text{ solving for I } \\ I=\frac{1157}{\mleft(0.88\mright)^3} \\ I=1697.79\cong1698 \end{gathered}$

(b)

Therefore, the function would be:

$P=1698\cdot(0.88)^t$

(c)

The number of bacteria after 10 days will be:

$\begin{gathered} P=1698\cdot(0.88)^{10} \\ P=472.89\cong473 \end{gathered}$