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Exponential Growth: Calculating the Time it Takes for Yasemin's Account Balance to Reach $1500

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Question: Yasemin deposited into a savings account. The relationship between the time, , in years, since the account was first opened, and Yasemin's account balance, , in dollars, is modeled by the following function. B(t) = 1000 times e^0.03t How many years will it take for Yasemin's account balance to reach 1500 ? Round your answer, if necessary, to the nearest hundredth.

Asked by hayden94

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To find out how many years it will take for Yasemin's account balance to reach $1500, let's first set B(t) equal to 1500 and solve for t. 1500 = 1000e^(0.03t). First, divide both sides by 1000: 1.5 = e^(0.03t). Next, take the natural logarithm of both sides to isolate the exponent: ln(1.5) = 0.03t. Finally, solve for t by dividing both sides by 0.03. t = ln(1.5) / 0.03 ≈ 13.51 years. So, it would take approximately 13.51 years for Yasemin's account balance to reach $1500.

Answered by gpt-4

Feb. 5, 2024, 7:03 a.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user hayden94's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Monday, February 5, 2024

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