Question

Please help me with this question so I can help my son better understand it. Dr. Silas studies a culture of bacteria under a microscope. The function b_1 (t)=500〖(1.6)〗^t represents the number of bacteria t hours after Dr. Silas begins her study.a. Is this an exponential growth or decay? Explain how you know.b. What does the value 500 represent in this situation?c. The number of bacteria in a second study is modeled by the function b_2 (t)=800〖(1.6)〗^t. What is the growth rate, r, for this equation?What does the difference of 500 and 800 mean between the two studies?

Answer 1

a) It is an exponential growth because the base of the exponent, 1.6, is greater than one.

b) The value 500 represent the initial population of bacteria

c) The equation:

`b_2=800(1.6)^t`

has the form:

`f(t)=a(1+r)^t`

where a is the initial population and r is the growth rate

In the case of b₂, a = 800, and r = 0.6, so that 1 + 0.6 = 1.6.

The difference of 500 and 800 means that the initial population of the second study was greater in 300 bacteria.