Question

Determine whether the following statements represent an exponential function or a linear function.1. • The average annual population of a pack of wolves increases each year by 25 wolves.•exponential function•linear function2. The value of a coin collection has increased by 3.25% annually over the last 20 years.•exponential function•linear function3. A population of bacteria decreases by a factor of ‡ every 24 hours.•exponential function•linear function4. For the first 6 training sessions, a personal trainer charges his clients $5 less than the previous training session.•exponential function•linear function5. The population of a certain country at time t' is represented by the function f(b) = 50000(1.02), 25.•exponential function•linear function

Answer 1

We want to determine if the questions are linear or exponential function

1. The average annual population of a pack of wolves increases each year by 25 wolves.

This means every year, the number of wolves increases by 25, that is 25 wolves is added to the initial number. That is previous number + 25 wolves.

Hence this is a linear function.

2. The value of a coin collection has increased by 3.25% annually over the last 20 years.

Percent rate of increase or decrease is an exponential function

Hence, this is an exponential function

3. A population of bacteria decreases by a factor of ‡ every 24 hours.

Bacteria population growth is always an exponential function.

Hence, this is an exponential function.

4. For the first 6 training sessions, a personal trainer charges his clients $5 less than the previous training session.

`\begin{gathered} So\text{ for the first 6 training, charges are} \\ (x-5)\text{ dollars } \\ \text{Let's say the previous was }x\text{ dollars } \end{gathered}`

So, this is a linear function

5. The population of a certain country at time t' is represented by the function

`f\mleft(t\mright)=50000\mleft(1.02\mright)^(.25t)`

From the function, you can clearly see the power or exponent, which is .25t

Hence, this is an exponential function