U4.L1.HW: Exponential Functions: Question 23

Question

Answer each of the blank lines and explain your answers afterwards.

The number of bacteria in a culture is given by the function 

n(t) = 989e^0.45t

where t is measured in hours.

(a) What is the continuous 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 ________

Round to the nearest bacteria.

Answer 1

Hi Manny Y

You can look up your given function n(t) and compare it to the Exponential Growth Formula to find the answers to most of your questions, please see below.

n(t)=980e^0.45t

P=P₀e^rt

Where

P=Final Population

P₀=Initial Population

r=rate of growth

t=time

e is just Euler’s number

In your function

n(t)=980e^0.45t

n(t)=Final Population at time t

980 = P₀, your initial Population

0.45 = r your rate written as a decimal, you just need to convert your decimal to percent to fill in a

t = time in hours

n(t)=980e^0.45t at t=0 recall the Rule for Exponents about anything raised to the zero power is 1

n(0)=980e^0.45(0) = 980e⁰ = 980(1) = 980 this confirms that your initial population is 980

n(5)=980e^0.45(5) = 980e^2.25= 9298 bacteria

I hope this helps, there are several other formulas for Exponential Growth that you can compare your function for example P(t)=P₀e^kt where k is the rate. You may have another that is available in your text or class that you can also compare to your function for labeling purposes.