Question

10. The table shows the balance of a money market account over time.

Write a function that represents the balance y (in dollars) after t years.
Write it in the form y=ab^t.*
Year, t Balance
0
$100
1
$125
2.
$156.25
3
$195.31
4
$244.14
5
$305.18

Answer 1

The function is
`y = 100 \cdot 1.25^t`

Explanation:

The table representing balance in the account is presented as follows;

Year
`{}` t

0
`{}` 100

1
`{}` 125

2
`{}` 156.25

3
`{}` 195.31

4
`{}` 244.14

5
`{}` 305.18

The given exponential relationship is y = a·b^t

When t = 0, y = 100

We get; 100 = a·b⁰ = a·1

∴ a = 100

When t = 1, y = 125

We get;

125 = 100·b¹

∴ b = 125/100 = 1.25

The function that represent 'y' (in dollars) after 't' years is y = 100×1.25^t