Answer:
[tex]\dfrac{1}{15}[/tex]
Step-by-step explanation:
Given that:
Investment amount = $2500
Time in which it gets doubled = 15 years
Amount after 15 years = $5000 (As per given statement as it gets doubled)
Value of investment in dollars after [tex]x[/tex] years if investment:
[tex]f(x) = 2, 500(2 ^ {rx})[/tex]
[tex]r[/tex] is a constant.
To find:
Value of [tex]r[/tex].
Solution:
We are given that:
[tex]f(x) =\$5000[/tex]
[tex]x=15\ years[/tex]
Putting all the values in the given equation:
[tex]5000 = 2500(2 ^ {r\times 15})\\\Rightarrow 2 = 2 ^ {r\times 15}\\\Rightarrow r\times 15=1\\\Rightarrow r =\bold{\dfrac{1}{15}}[/tex]
Therefore, the value of [tex]r[/tex] is:
[tex]\dfrac{1}{15}[/tex]
