QuestionJuly 22, 2025

Write a formula that describes the value of an initial investment of 1200 growing at an interest rate of 4% compounded continuously. a) A(t)=1200e^0.04t b) A(t)=1200e^4t c) A(t)=1200e^1.04t d) A(t)=1200(1.04)^t

Write a formula that describes the value of an initial investment of 1200 growing at an interest rate of 4% compounded continuously. a) A(t)=1200e^0.04t b) A(t)=1200e^4t c) A(t)=1200e^1.04t d) A(t)=1200(1.04)^t
Write a formula that describes the value of an initial investment of 1200 growing
at an interest rate of 4%  compounded continuously.
a) A(t)=1200e^0.04t
b) A(t)=1200e^4t
c) A(t)=1200e^1.04t
d)
A(t)=1200(1.04)^t

Solution
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Answer

a) A(t)=1200e^{0.04t} Explanation 1. Identify the correct formula for continuous compounding The formula for continuous compounding is **A(t) = P e^{rt}**, where P is the principal, r is the interest rate, and t is time. 2. Substitute given values into the formula Substitute P = 1200, r = 0.04 into the formula: A(t) = 1200 e^{0.04t}.

Explanation

1. Identify the correct formula for continuous compounding<br /> The formula for continuous compounding is **$A(t) = P e^{rt}$**, where $P$ is the principal, $r$ is the interest rate, and $t$ is time.<br /><br />2. Substitute given values into the formula<br /> Substitute $P = 1200$, $r = 0.04$ into the formula: $A(t) = 1200 e^{0.04t}$.
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