Question

In a laboratory experiment, the population of bacteria in a petri dish started off at 160 and is growing exponentially at 6% per hour. Write a function to represent the population of bacteria after t hours, where the rate of change per minute can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per minute, to the nearest hundredth of a percent.

Answer 1

The exponential function is given by y = 160(1.06)ˣ

Exponential function

An exponential function is in the form:

y = abˣ

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

Let y represent the amount of bacteria after x hours.

Given an initial 160 bacteria, hence a = 160.

Also b = 100% + 6% = 106% = 1.06

The exponential function is given by y = 160(1.06)ˣ

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