An investment of $9,000 earns interest at an annual rate of 6.5% compounded continuously. Complete A and B.(A) find the instantaneous rate of change of the amount in the account after 3 year(s). (Round to two decimal places as needed)(B) find the instantaneous rate of change of the amount in the account at the time the amount is equal to $13,000. (Round to two decimal places as needed)

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Asked Nov 4, 2019
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An investment of $9,000 earns interest at an annual rate of 6.5% compounded continuously. Complete A and B.

(A) find the instantaneous rate of change of the amount in the account after 3 year(s). (Round to two decimal places as needed)

(B) find the instantaneous rate of change of the amount in the account at the time the amount is equal to $13,000. (Round to two decimal places as needed)

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Expert Answer

Step 1

Use the following formula,

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A = Pe" Substitute P=9000, r=6.5% 6.5 A =9000e100

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Step 2

To find the instantaneous change,

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6.5 A =9000e10 6.5 d d 9000e100 dt -(A) dt 6.5 6.5 *100 A' 9000 100 6.5 A' = 585e100

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Step 3

For t=3...

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6.5 6.5 3 A' =585e100 585e0 - 710.95

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