Question

Suppose that $2500 is invested at interest rate k, compounded continuously, and grows to $4000.00 after 5 years. a. What is the interest rate?b. Find the exponential growth function. c. What will the balance be after 10 years? d. After how long will the $2500 have doubled?

Answer 1

\[A=Pe ^{rt}\]

\[4000 = (2500)e ^{5r}\]
divide both sides by 2500
\[1.6 = e ^{5r}\]
ln both
ln(1.6) = 5r div by 5
ln(1.6)/5 = r
.094 = r

function
\[A(t) = 4000e ^{.094t}\]

just substitute 10 in for t
\[A = 4000e ^{.094(10)}\]

for the doubling the amount must be 8000 so,
\[8000 = 4000e ^{.094t}\]

Answer 2

wow ty so much