Question

$4,300 is invested in an account earning 5.2% interest (apr), 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. answer attempt 1 out of 2 function: f(t) = ( )

Explanation:

Step1: Recall continuous compound formula

The formula for continuous compounding is $f(t) = Pe^{rt}$, where $P$ is principal, $r$ is APR, $t$ is time.

Step2: Substitute given values

$P = 4300$, $r = 0.052$. So $f(t) = 4300e^{0.052t}$. Round coefficients: $e^{0.052} \approx 1.0533$, but keep the continuous form as required, or format to match the structure: $f(t) = 4300(1.0533)^t$ is equivalent, but the strict continuous form is $f(t)=4300e^{0.052t}$. For the box structure, we use the continuous growth form with the coefficient rounded: $e^{0.052} \approx 1.0533$, so $f(t)=4300(1.0533)^t$ (or the exponential form with base $e$).

Step3: Calculate APY

APY for continuous compounding is $APY = e^r - 1$. Substitute $r=0.052$:
$APY = e^{0.052} - 1$
$APY \approx 1.0533 - 1 = 0.0533$, or 5.33%.

Answer:

Function: $f(t) = 4300e^{0.052t}$ (or formatted to match the box structure: $f(t) = 4300(1.0533)^t$)
Annual Percentage Yield (APY): 5.33%