joshua invests $500 at the interest rate show...
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)=500(1.039)^2t (simplify your answer. use integers or decimals for any numbers in the expression.) write the function for felixs investment in terms of time t. g(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 compounding $n$ times a year is $A = P(1+\frac{r}{n})^{nt}$, and for continuous compounding (exponential growth) is $A = Pe^{rt}$. Since the problem implies compounding, and for Felix, with an annual interest rate $r = 0.06$ and assuming annual compounding ($n = 1$), the principal $P=1000$.
## Step2: Write Felix's investment function
Substitute $P = 1000$, $r=0.06$ and $n = 1$ into the compound - interest formula $A(t)=P(1 + r)^t$. We get $g(t)=1000(1 + 0.06)^t=1000(1.06)^t$.
# Answer:
$g(t)=1000(1.06)^t$