The exponential equation for the growth is f(x)=57
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
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
=57
P=57
When x=1, population is 95.
f(1)=95
P
=95
57
=95
57=95/
----1
when x=5,population is 700.
f(5)=700
P
=700
57
=700
57=700/
-----2
Equating 1&2
95/
=700/![e^{5r}](https://tex.z-dn.net/?f=e%5E%7B5r%7D)
![e^{5x} /e^{x} =700/95](https://tex.z-dn.net/?f=e%5E%7B5x%7D%20%2Fe%5E%7Bx%7D%20%3D700%2F95)
=7.36
=7.36
=![(2.7182)^{2}](https://tex.z-dn.net/?f=%282.7182%29%5E%7B2%7D)
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}](https://tex.z-dn.net/?f=e%5E%7B0.5%2A21%7D)
=57![e^{10.5}](https://tex.z-dn.net/?f=e%5E%7B10.5%7D)
=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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