The balance in the account after x years is given by the function b(x)=625(1.015)^x.
To find the rate at which the balance increases per year, we can take the derivative of b(x) with respect to x:
b'(x) = 625 * (ln(1.015)) * (1.015)^x
The derivative represents the rate of change of the balance with respect to time. In this case, it represents the rate at which the balance increases per year.
To express this rate as a percentage, we can multiply b'(x) by 100:
rate = 100 * 625 * (ln(1.015)) * (1.015)^x
However, we can simplify this expression further. The value of ln(1.015) is approximately 0.0149. Plugging this in, we get:
rate ≈ 100 * 625 * 0.0149 * (1.015)^x
Simplifying this expression, we find:
rate ≈ 93.125 * (1.015)^x
Therefore, the balance in the account increases at a rate of approximately 93.125 * (1.015)^x percent per year.