Suppose that $15,000 is invested and at the end of 3yr, the value of the account is $19,356.92. Use the model A=Pe^(rt) to determine the average rate of return r under continuous compounding.

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Suppose that  $15,000 is invested and at the end of  3yr, the value of the account is  $19,356.92. Use the model  A=Pe^(rt) to determine the average rate of return  r under continuous compounding.

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Write Down Given Information: First, let's write down what we know: Initial investment (P) = $15,000 Final amount (A) = $19,356.92 Time (t) = 3 years We need to find the rate (r).Use Continuous Compounding Formula: We use the formula for continuous compounding: A = Pe^(rt). Let's plug in the values we know: $19,356.92 = $15,000 * e^(r*3).Solve for Rate: Now, we need to solve for r. Let's start by dividing both sides by $15,000. $19,356.92 / $15,000 = e^(r*3)Calculate Natural Logarithm: Calculate the left side: 19356.92 / 15000 = 1.290461333. So, 1.290461333 = e^(r*3).Apply Natural Logarithm Property: Next, we take the natural logarithm (ln) of both sides to get rid of the exponential. ln(1.290461333) = ln(e^(r*3))Calculate Natural Logarithm: The natural logarithm of e to the power of something is just that something, so: ln(1.290461333) = r*3Divide to Solve for Rate: Calculate the natural logarithm of 1.290461333: ln(1.290461333) ≈ 0.2552725051. So, 0.2552725051 = r*3.Calculate Average Rate of Return: Now, divide both sides by 3 to solve for r. 0.2552725051 / 3 = rCalculate r: 0.2552725051 / 3 ≈ 0.08509083503. So, r ≈ 0.08509083503, which is the average rate of return.

Suppose that $\$ 15,000$ is invested and at the end of $3 \mathrm{yr}$ , the value of the account is $\$ 19,356.92$ . Use the model $A=P e^{r t}$ to determine the average rate of return $r$ under continuous compounding.

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Suppose that $15,000 \$ 15,000 $15,000 is invested and at the end of 3yr 3 \mathrm{yr} 3yr, the value of the account is $19,356.92 \$ 19,356.92 $19,356.92. Use the model A=Pert A=P e^{r t} A=Pert to determine the average rate of return r r r under continuous compounding.

Suppose that $\$ 15,000$ is invested and at the end of $3 \mathrm{yr}$ , the value of the account is $\$ 19,356.92$ . Use the model $A=P e^{r t}$ to determine the average rate of return $r$ under continuous compounding.