Final answer:
To determine how long it would take for Kelly to have $800 in the account, we can set up and solve an exponential equation. The equation is 500 * (2^(t/7)) = 800, where t represents the number of years it takes for the amount to double. Solving for t gives us approximately 3.66 years.
Step-by-step explanation:
To determine how long it would take for Kelly to have $800 in the account, we need to find the number of times the amount doubles. Since the amount doubles every 7 years, we can represent this as an exponential equation:
500 * (2^(t/7)) = 800
Where t represents the number of years it takes for the amount to double. To solve for t, we can divide both sides of the equation by 500 and take the logarithm of both sides:
(2^(t/7)) = 1.6
t/7 = log(1.6)
t = 7 * log(1.6)
The value of t is approximately 3.66 years. Therefore, it would take Kelly approximately 3.66 years to have $800 in the account.