12. [-/4 Points] DETAILS MY NOTES HARMATHAP12 5.1.036. If $$ \$ 1000 $$ is invested for $$ x $$ years at $$ 9 \% $$, compounded continuously, the future value that $$ S=1000 e^{0.09 x} $$. What amount will result in 7 years? (Round your answer to the nearest cent.) $$ \$ $$ Need Help? Read II

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To find the future value $$ S $$ after 7 years with an initial investment of $$ \$1000 $$ at a continuous compounding rate of $$ 9\% $$, we can use the formula:

$$
S = 1000 e^{0.09 x}
$$

where $$ x $$ is the number of years. In this case, $$ x = 7 $$.

Now, we can substitute $$ x $$ into the formula:

$$
S = 1000 e^{0.09 \times 7}
$$

Calculating $$ 0.09 \times 7 $$:

$$
0.09 \times 7 = 0.63
$$

Now, we can substitute this value back into the equation:

$$
S = 1000 e^{0.63}
$$

Next, we need to calculate $$ e^{0.63} $$. Using a calculator, we find:

$$
e^{0.63} \approx 1.8746
$$

Now, we can calculate $$ S $$:

$$
S = 1000 \times 1.8746 \approx 1874.60
$$

Thus, the amount that will result after 7 years is approximately:

$$
\boxed{1874.60}
$$
The amount after 7 years is approximately \$1874.60.

[-/4 Points] DETAILS MY NOTES HARMATHAP12 5.1.036.
If is invested for years at , compounded continuously, the future value that
.
What amount will result in 7 years? (Round your answer to the nearest cent.)
Need Help? Read II

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[-/4 Points] DETAILS MY NOTES HARMATHAP12 5.1.036. If is invested for years at , compounded continuously, the future value that . What amount will result in 7 years? (Round your answer to the nearest cent.) Need Help? Read II