An initial investment of $3 is worth $147 after 5 years.
If the annual growth reflects a geometric sequence, approximately how much will the investment be worth after 11 years?
Select one:
a. 50421
b. 19057
c. 327
d. 363
To determine the value of the investment after 11 years, we can use the formula for a geometric sequence, which is given by:
A = P * r^n
Where:
A is the final amount
P is the initial amount
r is the common ratio
n is the number of years
We are given that the initial investment, P, is $3 and the number of years, n, is 5. We are also given the final amount, A, which is $147. To find the common ratio, we can rearrange the formula as follows:
A = P * r^n
$147 = $3 * r^5
Now, we can solve for r:
r^5 = $147/$3
r^5 = 49
r = 49^(1/5)
Using a calculator, we find that r is approximately 1.714.
Finally, we can plug the values of P, r, and n into the formula to find the investment's worth after 11 years:
A = P * r^n
A = $3 * (1.714)^11
Using a calculator, we find that the investment will be worth approximately $19,057 after 11 years.
Therefore, the answer is b. 19057.
3r^5/3 = r^5 = 147/3
so, 3r^11 = 3 (147/3)^(11/5) = ?
I suspect a typo