Question

I'm unsure of the best way to approach this exponential word problem and turn it into a functional equation

Answer 1

From the question;

A sample of bacteria is growing at an hourly rate of 6%

This means

Rate of growth = 6%

The sample began with 15 bacteria

We are to find how many bacteria will be in the sample after 18 hours

This will be done by using exponential growth formula

$A=P(1+\frac{r}{100})^{t^{}}$

Where

p = initial number of bacteria

r = rate of growth

t = time

A = new number of bacteria

From the question

$p=15,r=6\text{\%, t = 18, }$

Hence we have

$A=15(1+\frac{6}{100})^{18}$

By simplifying further we have

$\begin{gathered} A=15(1+0.06)^{18} \\ A=15(1.06)^{18} \\ A=15(2.854) \\ A=42.815 \\ A=43(to\text{ the nearest whole number)} \end{gathered}$

Therefore,

There will be 43 bacteria after 18 hours