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Kevin invested $\$1,000$ in a savings account with a daily interest rate of $0.1\%$ . Write an exponential function to represent the total amount, $s(x)$ , in his account after $x$ days.

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Write exponential functions: word problems

Full solution

Q. Kevin invested

\$1,000

in a savings account with a daily interest rate of

0.1\%

. Write an exponential function to represent the total amount,

s(x)

, in his account after

x

days.

Identify Principal and Rate: Identify the initial amount (principal) and the daily interest rate. $\newline$ The initial amount, $a$ , is $\$1,000$ . $\newline$ The daily interest rate, $r$ , is $0.1\%$ .
Convert to Decimal: Convert the daily interest rate from a percentage to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $r = 0.1\% = \frac{0.1}{100} = 0.001$
Determine Growth Factor: Determine the growth factor $b$ . The growth factor is $1$ plus the daily interest rate in decimal form. $b = 1 + r$ $b = 1 + 0.001$ $b = 1.001$
Write Exponential Function: Write the exponential function using the initial amount and the growth factor. $\newline$ The exponential function is in the form $s(x) = a(b)^x$ . $\newline$ Substitute $\$1,000$ for 'a' and $1.001$ for 'b'. $\newline$ $s(x) = 1000(1.001)^x$

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