Question

question
$6,600 is invested in an account earning 3.7% 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
function: $f(t) = \quad (\quad)$
growth ~ % increase per year
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Explanation:

Step1: Recall continuous growth formula

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

Step2: Plug in given values

Substitute $P=6600$, $r=0.037$:
$f(t) = 6600e^{0.037t}$
Calculate $e^{0.037} \approx 1.0377$ (to 4 decimals), so $f(t) = 6600(1.0377)^t$

Step3: Calculate APY

APY is $(e^r - 1) \times 100\%$.
$\text{APY} = (e^{0.037} - 1) \times 100\%$
$\text{APY} \approx (1.0377 - 1) \times 100\% = 3.77\%$

Answer:

Function: $f(t) = 6600(1.0377)^t$
% increase per year: $3.77\%$