Respuesta :
The exponential equation for the growth is f(x)=57[tex]e^{0.51x}[/tex] 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[tex]e^{rt}[/tex] 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[tex]e^{0}[/tex]=57
P=57
When x=1, population is 95.
f(1)=95
P[tex]e^{r}[/tex]=95
57 [tex]e^{r}[/tex]=95
57=95/[tex]e^{r}[/tex]----1
when x=5,population is 700.
f(5)=700
P[tex]e^{5r}[/tex]=700
57[tex]e^{5r}[/tex]=700
57=700/[tex]e^{5r}[/tex]-----2
Equating 1&2
95/[tex]e^{r}[/tex]=700/[tex]e^{5r}[/tex]
[tex]e^{5x} /e^{x} =700/95[/tex]
[tex]e^{5r-r}[/tex]=7.36
[tex]e^{4r}[/tex]=7.36
[tex](2.7182)^{4r}[/tex]=[tex](2.7182)^{2}[/tex]
equating both sides
4r=2
r=0.5
put the value of t=21 in the exponential equation
f(21)=57[tex]e^{0.5*21}[/tex]
=57[tex]e^{10.5}[/tex]
=57*36315.5
=2069983.5
Hence the population on 21st march is 2069983.5.
Learn more about equation at https://brainly.com/question/2972832
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