Five years ago Wendy invested 12000 into a mutural fund and

Five years ago, Wendy invested $12,000 into a mutural fund, and now the fund is worth $15,000, LET v (t) denote the value of the mutural fund after t years, with t =0 corresponding to the time the fund was originally purchased.

Solution

a) V(t) = mt+b

V(t) = 15000 $

t = 5 years

b = 12000$

15000 = m*5 + 12000

15000 - 12000 = 5m

3000 = 5m

m =3000/5

m = 600

Annual growth rate = 600$

b) f(x) = Ab^x

f(x) = 15000$

x = 5 years

A = 12000

15000 = 12000*(b)⁵

15000/12000 = b⁵

5/4 = b⁵

log (5/4) = 5 log b

0.0969/5 = logb

0.193 = logb

b = 10^0.193

b = 1.55

or

5/4 = b^5

(5/4)^(1/5) = b

b = 1.55