So confused

which situations can be represented by an exponential function? select each correct answer.

on the highway, kareem's car gets 38 mpg.

shu fang has $25.75 deducted from her checking account every month.

a toad population is increasing by about 7.5% each year.

an event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.

A toad population is increasing by about 7.5% each year.

An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.

Step-by-step explanation:

On the highway, Kareem's car gets 38 mpg.

This can be modeled with a linear relationship between the miles and the gallons of fuel needed.

Shu Fang has $25.75 deducted from her checking account every month.

Here we know that each month a constant amount is deducted from her, this is not an exponential relation.

A toad population is increasing by about 7.5% each year.

If the population initially was an amount P, after one year the population is P*1.075, after two years the population is P*(1.075)^2 and so on, this can be modeled with an exponential function where the years variable, the function will have the general form:

Population(y) = P*(1.075)^y

An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.

If the first year the population is X, the year after the attendance will be (4/5)X, and the year after this process applies again, so you have a 4/5 of the previous attendance, the attendance now is (4/5)^2*X

This also can be modeled with an exponential function, of the shape:

Attendance (y) = X*(4/5)^y, where again, y means years.

The thing you may notice is that in this case the model only works for the lapse of 5 years that the event organizer said.

x=6 and x=3

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