Question

Let f(t) = Q0at = Q0(1 + r)t.
f(7) = 75.94 and f(9) = 91.89
(a) Find the base, a. (Round your answer to two decimal place.)
a =


(b) Find the percentage growth rate, r. (Round your answer to the nearest percent.)
r = %



I honestly have no idea how to approach these problems. I wrote out the different equations:
75.94 = Q0a^7 and
91.89 = Q0a^9 but I don't know where to go from here for the first part.

For the second part of the question, I'm assuming that you plug in the values to the r equation so it would be:

75.94=Q0(1+r)^7 and
91.89=Q0(1+r)^9 but once again, I do not know where to go from here.

Should I use a system of equations?

Answer 1

I will try to reverse engineer what you are doing because I am not sure I understand you
Say we are doing a compound interest problem. Yearly interest rate as a decimal is r
For example 5% is .05
then every year I multiply what I have is the amount from the year before + r times the amount from the year before
or
Yn+1 = Yn + r Yn = Yn (1+r)

if Y0 = a
then Y1 = a(1+r)
and Y2 = a(1+r)(1+r) = a(1+r)^2
Yn = a (1+r)^n
so
Y9 = 91.89 = Y7(1+r)(1+r)
or 91.89 = 75.94 (1+r)^2
so
(1+r)^2 = 1.21
1+r = 1.10
r = .1 or 10 percent
now for a
y9 = 91.89 = a(1+r)^9 = a (1.1)^9
so a = 91.89/2.358 = 38.97
so I started with $38.97
compounded at 10% yearly
and after nine years had 91.89