Question

In a lab, a scientist is growing bacteria for a study. The scientist begins with a bacteria

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The growth of the bacteria is in the form of an exponential growth. It is given by the formula:

$P(t)=ae^{rt}\\\\where\ t\ is\ the\ number\ of \ hours, P(t)\ is\ the \ population\ at\ t\ hours\\\and\ a=population\ at\ start$

At 2 hours, the population is 62 cells, hence:

$P(2)=ae^{2r}\\\\62=ae^{2r}\ \ .\ \ .\ \ .\ (1)$

After another 2 hours (4 hours), the population is 1 million:

$P(4)=ae^{4r}\\\\1000000=ae^{4r}\ \ .\ \ .\ \ .\ (2)\\\\Divide \ equation\ 2\ by\ equation\ 1:\\\\\frac{1000000}{62}=\frac{ae^{4r}}{ae^{2r}} \\\\16129=e^{2r}\\\\ln(e^{2r})=ln(16129)\\\\2r=9.688\\\\r=4.844$

Put r = 4.844 in equation 1

$62=ae^{2*4.844}\\\\62=16129a\\\\a=0.003844$

$P(t)=0.003844e^{4.844t}\\\\at \ start,t=0\\\\P(0)=0.003844$