9514 1404 393
Answer:
b. 11 years
Step-by-step explanation:
Since we're interested in the time going forward, we can write the expnential function for Rosa's balance as ...
y = 4500(4500/2000)^(x/6)
where x is the number of years from now, and y is the balance at that time.
20,000 = 4,500(2.25^(x/6))
Dividing by 4500, we get ...
40/9 = 2.25^(x/6)
log(40/9) = (x/6)log(2.25) . . . . take logs
x = 6·log(40/9)/log(2.25) ≈ 11.037 . . . . divide by the coefficient of x
It will take 11 more years for Rosa to have $20,000 in the bank.
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Comment on the exponential function
You can generally write an exponential function for a question of this sort pretty easily. The form of it is ...
f(t) = (initial value)×(growth factor)^(t/(growth period))
Here, we're given a growth factor of 4500/2000 = 2.25 corresponding to a period of 6 years. This tells us t is in years, and the exponential term will be ...
2.25^(t/6)
The "initial value" we choose corresponds to t=0. Since we want 'years from now', the "initial value" will be the value in the account now, 4500.
