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Exponential and Logarithmic Functions
Finding the time in a word problem on compound interest
Morg:
Teresa needs for a future project. She can invest now at an annual rate of , compounded monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
years
Studdy Solution
Solve for the unknown variable, .
First, simplify the expression inside the parentheses:
Now, substitute back into the equation:
Divide both sides by 4000 to isolate the exponential term:
Calculate the left side:
Take the natural logarithm of both sides to solve for :
Using the logarithmic identity , we have:
Solve for :
Calculate the value of :
The time it will take for Teresa's investment to grow to $6260 is approximately \( \boxed{4.16} \) years.
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