Answer:
28.5 years
Step-by-step explanation:
You want to know how many years it takes for a $210 investment to have a value of $1510 if it doubles in value every 10 years.
Doubling
When an account doubles in value in 10 years, its value after t years is given by ...
A = P(2^(t/10))
We have A=1510, P=210, and we want to find t.
Solution
1510 = 210(2^(t/10)) . . . . . . use the given values
1510/210 = 2^(t/10) . . . . . divide by 210
Taking logarithms gives ...
log(1510/210) = (t/10)log(2)
Dividing by the coefficient of t, we have ...
t = 10·log(1510/210)/log(2) ≈ 28.46
It would take about 28.5 years for the value of the account to reach $1510.
