Question

Under a microscope, ms. kapinski studies a culture with bacteria. as the number of hours progresses, ms. kapinski sees that the bacteria can be modeled by the function b(t)=1290(0.76)^t where b represents the number of bacteria t hours after ms. kapinski begins her study.

what does the value 0.76 represent in this situation? be sure to explain.
what does the value 1290 represent in this situation? be sure to explain.

the number of bacteria in a second study is modeled by the function b_2 (t)=1180(1.76)^t.

what does the value of 1180 represent in this situation?
what does the difference of 1290 and 1180 mean between the two studies?
what does the difference between 0.76 and 1.76 mean between the two studies?

Answer 1

Study 1 Answers:

1) 0.76 represents the multiplier of the bacteria, in this case it is decreasing by 24% because the formula for exponential decay is 1 - r.

2) 1290 represents the initial value, or before the study began.

Study 2 Answers:

1) 1180 is the initial value, or before the study began.

2) Study 1 started with more bacteria

3) Study 1 is experiencing exponential decay, while study 2 is experiencing exponential growth

Explanation:

Exponential functions are in the form
`y=a(b)^x`, where a is the initial value, b is the multiplier, and x represents inputs, such as hours after a bacteria study.

Any multiplier above 1.00 is experiencing exponential growth, meaning it grows gradually over time, and any multiplier below 1.00 is experiencing exponential decay, meaning it decreases in population over time.