Question

Stephanie found that the number of white-winged cross bills in an area can be represented by the formula C = 550(1.08)t, where t represents the number of years since 2010. Which equation correctly represents the number of white-winged cross bills in terms of the monthly rate of population growth?

1) C = 550(1.00643)t
2) C = 550(1.00643)12t
3) C = 550(1.00643)t/12
4) C = 550(1.00643)t + 12

Answer 1

Option 2)
`C = 550(1.00643)^(12t)`

Explanation:

Given : The number of white-winged cross bills in an area can be represented by the formula C = 550(1.08)^t

General Growth Formula:
`A = P(1 + r)^t`

where, A = Amount after growth

P = Original amount

r = yearly growth rate

t= number of years

Comparing Formula C with the general formula:

A=C, P=550, t=t and (1+r)=1.08⇒r=0.08

Now, we have to find the equation represent the number of white-winged cross bills in terms of the monthly rate of population growth.

For monthly, the rate is divided by 12 and time is multiply by 12.

i.e,
`t= 12* t=12t` and
`r=(0.08)/(12)=0.006`

The new equation formed →
`C = 550(1 + 0.006)^(12t)`

`C = 550(1.006)^(12t)`

From the following formula option 2) is matched

Therefore, Option 2) is the correct answer.