Question

A bacteria population increases exponentially at a rate of r% each day. After

Answer 1

Answer:

r=4.5% daily

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

$P=P_o(1+r)^t$

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.

Substitute the given values into the model function:

$409\%P_o=100\%P_o(1+r)^{32}$

Simplifying:

$4.09=(1+r)^{32}$

We need to solve for r. Taking the 32nd root:

$\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}$

Simplifying:

$1+r=\sqrt[32]{4.09}=1.045$

Solving:

$r=1.045-1\Rightarrow r=0.045$

r=4.5% daily