The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. the initial price of one share was $102.15. an investor plans to sell once the value of one share reaches $233.10. if t is the number of quarters since the initial price of one share was set, which equation could be used to determine how long it will take the share to reach $233.10, assuming it continues to grow at the same rate?

39 quarter

The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. That means the stock will increase by 8.6%/4= 2.15% rate per quarter. The exponent function to find the number of money the investor have would be:
an= $102.15(1.0215)^t

The time needed for getting $233.10 would be:

an= $102.15(1.0215)^t
$233.10= $102.15(1.0215)^t
2.2819 * $102.15= $102.15( 1.0215)^t
2.2819 = (1.0215)^t
t= log1.0215 2.2819
t= 39