Question

Sherrie's biology class is studying the ability of a certain microbe to dissipate oil spilled in seawater. to be effective the population of microbes must grow exponentially. she has recorded the microbe population growth as follows: # days after march 1st 0, 1, 5, 10 population 57, 95, 700, 8525 a. using sherrie's data, find the best exponential equation for this growth using the substitution method. must show work. b. using the same data get an equation using calculator's regression feature. then estimate the microbe population on march 21st

Answer 1

The exponential equation for the growth is f(x)=57$e^{0.51x}$ where x is the number of days and the population on 21st march is 2069983.5 of microbes.

Given:

Days                   population

0                                57

1                                 95

5                               700

10                               8525

We have to form exponential equation which shows the growth of microbes.

We know that exponential equation which shows the sum is as under:

f(x)=P$e^{rt}$ where r is the rate of growth and x is the number of days, months or years depending on how things grows.

In the question when x=0 population is 57.

f(0)=57

P$e^{0}$=57

P=57

When x=1, population is 95.

f(1)=95

P$e^{r}$=95

57 $e^{r}$=95

57=95/$e^{r}$----1

when x=5,population is 700.

f(5)=700

P$e^{5r}$=700

57$e^{5r}$=700

57=700/$e^{5r}$-----2

Equating 1&2

95/$e^{r}$=700/$e^{5r}$

$e^{5x} /e^{x} =700/95$

$e^{5r-r}$=7.36

$e^{4r}$=7.36

$(2.7182)^{4r}$=$(2.7182)^{2}$

equating both sides

4r=2

r=0.5

put the value of t=21 in the exponential equation

f(21)=57$e^{0.5*21}$

=57$e^{10.5}$

=57*36315.5

=2069983.5

Hence the population on 21st march is 2069983.5.

Learn more about equation at brainly.com/question/2972832

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