Exponential Equations 20

Question

The number of bacteria in a culture is given by the functionwhere  is measured in hours.

(a) What is the relative rate of growth of this bacterium population?Your answer is_____    percent?

(b) What is the initial population of the culture (at t=0)?Your answer is  ____ ?

(c) How many bacteria will the culture contain at time t=5?Your answer is _____?  

Answer 1

Hi Stephanie! To help answer your question, you need to be familiar with the exponential growth formula A=Pe^rt. Here, P represents the initial population, e is the mathematical constant (approximately 2.718), r is the growth or decay rate as a decimal, and t is the time.

For part a, you need to compare your given function with the exponential growth formula. To help you, your original function would be typed more properly as n(t)=950e^0.15t. Think about which part of your function corresponds with the growth rate in the formula.

For parts b and c, it is asking you to use the function they gave you to find specific output values. For example, part b is asking you to find the population at t=0, which means that you can plug 0 into the function for t. When you do this, remember that e is a constant (similar to π). There is a button on your calculator to use the exact number e, or you can use a decimal approximation of 2.718.

I hope this helps you! Please reach out if you have any follow-up questions.