Answer:
The function have a constant ratio
No, it does not represent an exponential function.
Step-by-step 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 = [tex]\frac{b}{a} = \frac{c}{b}[/tex]
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 = [tex]\frac{10}{5} (=2) = \frac{20}{10}(=2)[/tex]
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.
