Use the continuous change function A (t) = Pert to answer the question.

Question

You invest $2,500 in an account that grows 5% each year What will be your investment amount after 6 years?

(1 point)

Ο $2,699.72

$3,374.65

$15,769.07

$13,272.96

Answer 1

To use the continuous growth function $A(t)=P{e}^{rt}$, where:

• $P$ is the principal amount (initial investment),
• $r$ is the annual interest rate (as a decimal),
• $t$ is the time in years,
• $e$ is the base of the natural logarithm (approximately equal to 2.71828).

Given:

• $P=2500$
• $r=0.05$ (5% expressed as a decimal)
• $t=6$

Now, plug these values into the formula:

$$A(6)=2500\cdot e^{0.05\cdot 6}$$

Calculating $0.05\cdot 6=0.30$:

So, we need to find $e^{0.30}$:

Using a calculator (or an approximation),

$$e^{0.30}\approx 1.34986$$

Now plug this back into the formula:

$$A(6)=2500\cdot 1.34986\approx 3374.65$$

Thus, the investment amount after 6 years will be approximately $3,374.65.

The answer is $3,374.65.