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A population of bacteria is growing according to the equation P(t) = 1850e ^ (0.09t). Estimate when the population will exceed 2402t=Give your answer accurate to one decimal place.

Sagot :

We will have the following;

[tex]\begin{gathered} 2402=1850e^{0.09t}\Rightarrow\frac{2402}{1850}=e^{0.09t}\Rightarrow\frac{1201}{925}=e^{0.09t} \\ \\ \Rightarrow ln(\frac{1201}{925})=0.09t\Rightarrow t=\frac{ln(1201/925)}{0.09} \\ \\ \Rightarrow t=2.901289829...\Rightarrow t\approx2.9 \end{gathered}[/tex]

So, the population will exceed 2402 bacteria after 2.9 units of time.

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