3.1k views
3 votes
6 years ago Rosa had $2,000 in the bank. She now has $4,500. The amount of money at the end of each year increases exponentially. How many more years (to the nearest year) will pass before Rosa has $20,000 in the bank? (Assume that she doesn't deposit or withdraw any money.)

a. 7 years
b. 11 years
c. 17years
d. 39 years

2 Answers

2 votes

Answer:

B 11 years

Explanation:

User Marc Enschede
by
8.5k points
4 votes

9514 1404 393

Answer:

b. 11 years

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.

_____

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.

User Zorina
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.