Question

A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his experiment with 500 bacteria that grow at a rate of 16% per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours? Round your answer to the nearest whole number.

Answer 1

The population of the bacteria after 8 hours is 1639 bacteria.

An exponential function is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population of bacteria after x hours.

Given that he starts his experiment with 500 bacteria, hence

a = 500

The bacteria grow at a rate of 16% per hour, hence:

b = 100% + 16% = 1.16

The exponential equation becomes:

y = 500(1.16)ˣ

After 8 hours:

y = 500(1.16)⁸ = 1639

The population of the bacteria after 8 hours is 1639 bacteria.

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