Question

The number of bacteria, B(h), in a certain population increases according to the following

function, where time, h, is measured in hours:
B(h) = 1425 e ^0.15h
How many hours will it take for the bacteria to reach 3300?
Round your answer to the nearest tenth, and do not round any intermediate
computations.


Please helpppp!!!

Answer 1

It will take 5.6 hours to get the given population (3300) of the bacteria.

Explanation:

A function that defines the population increase of a bacteria is,

B(h) =
`1425e^(0.15h)`

where h = duration or number of hours for bacterial growth

B(h) = Final population

If the final bacterial population is 3300,

3300 =
`1425e^(0.15h)`

By taking log on both the sides of the equation,

ln(3300) =
`ln(1425e^(0.15h))`

8.10168 = ln(1425) +
`ln(e^(0.15h))`

8.10168 = 7.261927 + 0.15h

h =
`(8.10168-7.261927)/(0.15)`

h = 5.5983

h ≈ 5.6 hours

Therefore, it will take 5.6 hours to get the given population (3300) of the bacteria.