Mathematics: A bacteria population increases exponentially at a rate of r% each day. After 32 days, the population has increased by 309%. Find the value of r.

(39x52=2028) (3.8x62=18.62) 2028 divided by 18.62 equals (108.915145) 108.91...

A bacteria population increases exponentially at

rmartinez044

03.02.2022

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

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