Question

Ines has saved $5. She doubles the amount she saves each week. Does the function have a constant difference or a constant ratio? Does this represent an exponential function?

Answer 1

The function have a constant ratio

No, it does not represent an exponential function.

Explanation:

As given,

Ines has saved $5. She doubles the amount she saves each week.

⇒ In first week she saved = $5

In second week she saved = 2×$5 = $10

In third week she saved = 2×$10 = 20

In fourth week she saved = 2×$20 = 40

and so on..

∴ we get the series

5, 10, 20, 40 ,.......

If the series is given as a, b, c, d, ..... , then

The common difference is defined as d = b-a = c-b

The common ration is defined as r =
`(b)/(a) = (c)/(b)`

Here, in the given question

The series is - 5, 10, 20, 40

This has no common difference , d = 10 - 5 (= 5 )≠ 20 - 10 (= 10)

As 5 ≠ 10

So the function does not define common difference .

Now,

This has common ratio , r =
`(10)/(5) (=2) = (20)/(10)(=2)`

As 2 = 2

So, the function represent common ratio

Now,

The function does not represent an exponential function because it is increased by common ratio.