SOLUTION: A) suppose $4000 is invested at rate k, compounded continuously, and grows to $4555.31 in 5 years.
1) find the exponential growth function.
2) find the balance afte
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Question 889213: A) suppose $4000 is invested at rate k, compounded continuously, and grows to $4555.31 in 5 years.
1) find the exponential growth function.
2) find the balance after 10 years.
B) to create a college fund, a parent makes a sequence of 15 yearly deposits of $1200 each in a savings account on which interest is compounded annually at 3.5%. Find the total amount saved in the fund.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
4555.31 = 4000 * e^(5k)
divide both sides by 4000 to get:
4555.31/4000 = e^(5k)
take natural log of both sides of the equation to get:
ln(4555.31/4000) = ln(e^(5k)
since ln(e^(5k) = 5k*ln(e) = 5k*1 = 5k, you get:
ln(4555.31/4000) = 5k
divide both sides by 5 to get:
k = ln(4555.31/4000) / 5 = .0259998449
set up new equation for 10 years.
y = 4000 * e^(10k)
replace k to get:
y = 4000 * e^(10*.0259998449) to get:
y = 5187.712299
your answer are:
k = .0259998449
value after 20 years = 5187.712299
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