Question

1) Which equation could be used to estimate the population of Oak City in 10 years?

A) y = 48000(1.024)10
B) y = 48000(0.024)10
C) y = 48000(1.24)10
D) y = 48000(10.24)10

2) Which equation could be used to estimate Johnson City's population in 5 years?
A) y = 82000(1.983)5
B) y = 82000(0.983)5
C) y = 82000(−0.017)5
D) y = 82000(98.3)5

Answer 1

1) A

2) B

Explanation:

For this problem we use exponential growth formulas

`y = y_0(1 + r) ^ t` if the population increases when t increases

`y = y_0(1-r) ^ 2` If the population decreases when t increases

Where and is the population as a function of time,
`y_0` is the initial population, r is the growth rate, t is the time in years.

1) In this situation we have that
`y_0 = 48000`, the growth is 2.4%, then
`r = 0.024` and
`t = 10` and the equation is:

`y = 48000(1 + 0.024) ^ {10}`

`y = 48000(1.024) ^ {10}` -------- Option A)

2) In this situation we have that
`y_0 = 82000`, the decrease is 1.7%, then
`r = 0.017` and
`t = 5` and the equation is:

`y = 82000(1-0.017) ^ 5`

`y = 82000(0.983) ^ 5` -------- Option B)