A person initially invests 70000 in a mutual fund After 4 ye

A person initially invests $70000 in a mutual fund. After 4 years the amount in the account is $96000.

(a) Find a function that models the amount in the account t years after the initial investment if you assume an exponential growth model, A ( t ) = ab^t.. Round b to four decimals. A ( t ) =

(b) Use the function from part (a) to find the amount in the account after 10 years.

Amount in account is $

Solution

A(t) = ab^t

where a is the intial invested amount = $ 70,000

b --growth factor

after t= 4yrs A(t) = 96000

96000 = 70,000(b)^4

b^4 = 1.37

b= (1.37)^1/4

b = 1.082

a) So, A(t) = 70,000(1.082)^t

b) Amount aftre t= 10yrs

A(10) = 70,0000(1.082)^10 = $154181.058 = $154181