The rate at which the money is growing is exponential. The formula for determining such exponential growth is expressed as
A(t) = Pe^rt
Where
A(t) represents the amount after t years
P represents the initial amount
t represents the number of years
r represents the growth rate
Given that the amount doubles after 6 years, it means that
when t = 6, A(t) = 7400 * 2 = 14800
Recall, P = 7400
Thus, the expression becomes
14800 = 7400e^6t
14800/7400 = e^6t
2 = e^6t
Taking natural logarithm of both sides of the equation, it becomes
ln 2 = ln e^6t = 6t lne
Recall, ln e = 1
Thus, we have
ln 2 = 6t
t = ln2/6 = 0.1155
The equation would be
A(t) = 7400e^0.1155t
When t = 4, it becomes
A(t) = 7400e^0.1155*4
A(t) = 11745.62
Rounding to the nearest dollar, the amount in the account after 4 years is
$11746