Question

James is trying to save money for college. When

he is 5 years old, his uncle puts $750 into a
savings account for him. The money should
increase by 5% each year until he needs it for
college.
Write an exponential model for this situation.

Answer 1

`y=(750)1.05^t`, where
`t` is the time (in years) from investment

Or
`y=(750)1.05^(t-5)`, where
`t` is the age of James

Explanation:

exponential model:
`y=ab^t`, where
`t` is the time (in years) from investment

when t = 0, y = 750

`\implies 750=ab^0`

As
`b^0=1`

`\implies 750=a`

Therefore,
`y=750b^t`

If the savings increase by 5% each year, then b = 105%.

105% = 105/100 = 1.05

Therefore, b = 1.05

So final model:
`y=(750)1.05^t`, where
`t` is the time (in years) from investment

Or, we can write this as
`y=(750)1.05^(t-5)`, where
`t` is the age of James