Final answer:
The equation that represents the number of years (t) it takes $200 to grow to $500 at an exponential rate of 15% per year is option C. 500 = 200(1.15)^t. To solve this equation, divide both sides by 200, take the logarithm with base 1.15, and calculate the value of t.
Step-by-step explanation:
The equation that represents the number of years (t) it takes $200 to grow to $500 at an exponential rate of 15% per year is option C. 500 = 200(1.15)t.
To solve this equation, we need to isolate t. First, divide both sides of the equation by 200 to get 500/200 = (1.15)t. Then, take the logarithm of both sides with base 1.15 to solve for t. This gives us t = log1.15(500/200).
Using a calculator, we can find that t is approximately 1.956, which means it takes about 1.956 years for $200 to grow to $500 at a 15% annual growth rate.