Questions: 920 is invested in an account earning 7% interest (APY), compounded continuously. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY) to the nearest hundredth of a percent.

To solve this problem, we need to write a function that represents the value of an investment compounded continuously and determine the annual percentage yield (APY).

The formula for continuous compounding is given by:

\[ A(t) = P \cdot e^{rt} \]

where:

• \( A(t) \) is the amount of money accumulated after \( t \) years, including interest.
• \( P \) is the principal amount (initial investment), which is $920 in this case.
• \( r \) is the annual interest rate (as a decimal), which is 7% or 0.07.
• \( t \) is the time in years.
• \( e \) is the base of the natural logarithm, approximately equal to 2.71828.

Substituting the given values into the formula, we get:

\[ A(t) = 920 \cdot e^{0.07t} \]

Rounding the coefficients to four decimal places, the function becomes:

\[ f(t) = 920 \cdot e^{0.0700t} \]

The annual percentage yield (APY) for continuous compounding can be calculated using the formula:

\[ \text{APY} = e^r - 1 \]

Substituting \( r = 0.07 \):

\[ \text{APY} = e^{0.07} - 1 \]

Calculating this:

\[ e^{0.07} \approx 1.072508 \]

\[ \text{APY} = 1.072508 - 1 = 0.072508 \]

Converting this to a percentage and rounding to the nearest hundredth:

\[ \text{APY} \approx 7.25\% \]

The function representing the value of the account after \( t \) years is:

\[ f(t) = 920 \cdot e^{0.0700t} \]

The percentage of growth per year (APY) is approximately 7.25%.