document.write( "Question 1207164: Abby started with $12,000 in her savings account. The banks interest is 5% annual percentage rate compounded monthly. What is the model as an exponential growth function? \n" ); document.write( "

Algebra.Com's Answer #844874 by Shin123(626) $\"\"$ $\"About$

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Recall the compound interest formula, $\"P%281%2Br%2Fn%29%5E%28nt%29\"$ , where $\"P\"$ is the principal, $\"r\"$ is the interest rate (as a decimal), $\"t\"$ is the amount of years, and $\"n\"$ is how many times a year it is compounded. We know all of these variables except for $\"t\"$ , so it will be a function in terms of time. Plugging everything in, we get $\"12000%281%2B0.05%2F12%29%5E%2812t%29.\"$ To simplify it further and have the exponent be just $\"t\"$ , we can rewrite the function as $\"12000%28%281%2B0.05%2F12%29%5E12%29%5Et\"$ . The inner expression is $\"%281%2B0.05%2F12%29%5E12\"$ , and we can evaluate it to get the function as $\"12000%2A1.0511619%5Et\"$ (rounding the inner constant to 7 decimal places. If you want, you can calculate the expression to more decimal places, or just keep it as $\"12000%281%2B0.05%2F12%29%5E%2812t%29\"$ , depending on which one is better for you. \n" ); document.write( "

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