Question

Dr. Silas studies a culture of bacteria under a microscope. The function b1(t)=1200(1.8)6t represents the number of bacteria t hours after Dr. Silas begins her study.
(a) What does the value 1200 represent in this situation?
(b) What does the value 1.8 represent in this situation?
(c) The number of bacteria in a second study is modeled by the function b2(t)=1000(1.8)^t
What does the value of 1000 represent in this situation?
What does the difference of 1200 and 1000 mean between the two studies?

Answer 1

a) a = 1200 which is the initial population of the bacteria

b) b = 1.8 which represents the growth rate since it is greater than 1

What are exponential equations

Exponential equations are written as y = ab^x

• a is the initial population
• b is the rate (growth or decline)
• x is the time taken

• If b < 1, then it is a decline rate
• If b > 1 then it is a growth rate

Given the exponential function $b_1(t)=1200(1.8)^{6t}$

Compared with the general equation;

a) a = 1200 which is the initial population of the bacteria

b) b = 1.8 which represents the growth rate since it is greater than 1

For the exponential function $b_2(t)=1000(1.8)^t$

a) a = 1000 which is the initial population of the bacteria

b) The difference of 1200 and 1000 mean the difference between the initial populations.

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