The original number of bacteria found present in a body was 160. Now, after a period of 9 hours, the body has a count of 920 bacteria. Write the exponential equation that models the growth of the bacteria.

Nann

Nann

Answered question

2020-12-02

The original number of bacteria found present in a body was 160. Now, after a period of 9 hours, the body has a count of 920 bacteria. Write the exponential equation that models the growth of the bacteria.

Answer & Explanation

comentezq

comentezq

Skilled2020-12-03Added 106 answers

The general exponential model is:
y(t)=y0ert
where
y(t) is the amount of bacteria present in the body at time t.
y0 is the amount of bacteria at time t = 0.
r is the growth rate of bacteria.
Now initially the number of bacteria found in a body was 160, that is:
y0=160
Therefore:
y(t)=160ert
After a period of 9 hours, the body has a count of 920 bacteria, that is:
y(9)=920
160e9rt=920
e9r=920160
e9r=234
r=19ln(234)
r0.19435
Hence the exponential equation that models the growth of the bacteria is:
y(t)=160e0.19435t

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