An individual has $35,000 to invest: $24,000 will be put into a low-risk mutual fund averaging 6.7% interest compounded monthly, and the remainder will be invested in a high-yield bound fund averaging 9.2% interest compounded continuously. (a) Write an equation for the total amount, A, in the two investments after t years. A(t) = 24000(1.00558)' 12t + 11000e 0.092t dollars (b) Write the rate-of-change equation for the combined amount. (Round all numerical values to four decimal places.) A'(t) = dollars per year (c) How rapidly is the combined amount of the investment growing after 6 months? after 24 months? (Round your answers to the nearest cent.) 6 months $ per year 24 months $ per year

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
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An individual has $35,000 to invest: $24,000 will be put into a low-risk mutual fund averaging 6.7% interest compounded monthly, and the remainder will be invested in a high-yield bound fund
averaging 9.2% interest compounded continuously.
(a) Write an equation for the total amount, A, in the two investments after t years.
A(t) = 24000(1.00558) 127 + 11000e0.092t
dollars
(b) Write the rate-of-change equation for the combined amount. (Round all numerical values to four decimal places.)
A'(t) =
dollars per year
(c) How rapidly is the combined amount of the investment growing after 6 months? after 24 months? (Round your answers to the nearest cent.)
6 months
$
per year
24 months $
per year
Transcribed Image Text:An individual has $35,000 to invest: $24,000 will be put into a low-risk mutual fund averaging 6.7% interest compounded monthly, and the remainder will be invested in a high-yield bound fund averaging 9.2% interest compounded continuously. (a) Write an equation for the total amount, A, in the two investments after t years. A(t) = 24000(1.00558) 127 + 11000e0.092t dollars (b) Write the rate-of-change equation for the combined amount. (Round all numerical values to four decimal places.) A'(t) = dollars per year (c) How rapidly is the combined amount of the investment growing after 6 months? after 24 months? (Round your answers to the nearest cent.) 6 months $ per year 24 months $ per year
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