joshua invests $500 at the interest rate shown. felix invests $1,000 in an account with the same compounding…

joshua invests $500 at the interest rate shown. felix invests $1,000 in an account with the same compounding but at 6% interest rate. model each investment with an exponential growth function. whose money will double first? explain. write the function for joshuas investment in terms of time t. f(t)=□ (simplify your answer. use integers or decimals for any numbers in the expression.)

joshua invests $500 at the interest rate shown. felix invests $1,000 in an account with the same compounding but at 6% interest rate. model each investment with an exponential growth function. whose money will double first? explain. write the function for joshuas investment in terms of time t. f(t)=□ (simplify your answer. use integers or decimals for any numbers in the expression.)

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula for an exponential growth function is $A(t)=P(1 +\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. For Joshua, $P = 500$, $r=0.078$, and $n = 2$.

Step2: Substitute values into the formula

Substitute the values of $P$, $r$, and $n$ into the formula: $f(t)=500(1+\frac{0.078}{2})^{2t}$.

Step3: Simplify the expression inside the parentheses

First, calculate $\frac{0.078}{2}=0.039$. Then $1+\frac{0.078}{2}=1 + 0.039=1.039$. So, $f(t)=500(1.039)^{2t}$.

Answer:

$f(t)=500(1.039)^{2t}$