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1 point
A philanthropist pledges to donate
11% of a fund each year. If the fund initially has
$790000.00, how much will the fund have after 10 years?
$ type your añswer...

$1$ point $\newline$ A philanthropist pledges to donate $11 \%$ of a fund each year. If the fund initially has $\$ 790000.00$ , how much will the fund have after $10$ years? $\newline$ \$ type your añswer...

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Exponential growth and decay: word problems

Full solution

Q.

1

point

\newline

A philanthropist pledges to donate

11 \%

of a fund each year. If the fund initially has

\$ 790000.00

, how much will the fund have after

10

years?

\newline

\$ type your añswer...

Identify initial amount and percentage: Identify the initial amount and the percentage decrease per year. $\newline$ Initial amount $a$ = $\$790,000$ $\newline$ Percentage decrease per year $r$ = $11\%$
Calculate remaining percentage: Calculate the percentage that remains in the fund each year. $\newline$ Remaining percentage each year = $100\% - 11\% = 89\%$ $\newline$ Convert this to decimal form for calculation: $0.89$
Use exponential decay formula: Use the formula for exponential decay to find the amount after $10$ years. $\newline$ Formula: Final amount $=$ Initial amount $\times$ (Remaining percentage each year) $^{\text{number of years}}$
Plug in values and calculate: Plug in the values and calculate the final amount. $\newline$ Final amount = $\$790,000 \times (0.89)^{10}$
Calculate power of $0.89^{10}$ : Calculate the power of $0.89^{10}$ . $\newline$ $0.89^{10} \approx 0.3138$ (using a calculator)
Multiply initial amount by power: Multiply the initial amount by the calculated power to get the final amount. $\newline$ Final amount = $\$790,000 \times 0.3138$
Perform multiplication to find final amount: Perform the multiplication to find the final amount. Final amount $\approx$ $\$247,902$

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