grandma gigi gave leyla a rare purple stone for her sweet 16 birthday. at that time,the stone was worth$245. it has been increasing in value by the same percentage each year, when Leyla turned 21, the stone was worth $560.50. if s(t) represents the value in dollars of the stone t years after grandma Gigi gave it Leyla determine the value of a and r if s(t)=a(r)

Accepted Solution

This is a compound interest problem, therefore s(t) should be in the form:
[tex]s(t) = a(r)^{t} [/tex]

t = time in years
s(t) = the value of your item after t years
a = the initial value of your item
r = rate

Therefore, we already know that a = 245$.

Now, we can calculate r:
[tex] r^{t}=\frac{s}{a}[/tex]
[tex]r = \sqrt[t]{ \frac{s}{a} } [/tex]
[tex]r = \sqrt[5]{ \frac{560.50}{245} } [/tex]
     = 1.18

Therefore, the correct answers are a = 245 and r = 1.18