Need help solving exponential problem

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In summary, the conversation revolves around a question asking for help in solving an exponential problem. The problem involves finding the time needed to repay a loan of $10,000 with a monthly interest rate of 2.14% and monthly payments of $230. Different methods, such as the Newton-Raphson method, are suggested for solving the problem.
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Hi,

I'm new to this forum so thank you in advance for any help on this problem. I would like to understand the steps needed to solve this problem. The answer is 3.94111..286 = (1.00178^(12 * t))/t or .286 = (e^.021341 * t)/t
 
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  • #2
Re: need help solving exponential problem

Hi arrow, welcome to MHB!:)

In your question, I believe there's really no easy way(that I know of) to do it, but one can approximate its only solution by using the Newton-Raphson method, have you heard of this method before?
 
  • #3
Re: need help solving exponential problem

Hi Anemone,

No, I'm not familiar with this method. I'll take a look. Thanks.
 
  • #4
Re: need help solving exponential problem

arrow said:
Hi Anemone,

No, I'm not familiar with this method. I'll take a look. Thanks.

Oh okay...but would it be possible for you to restate the problem in its entirety here? We might be able to provide other useful advice to you if you post the full question for us first...
 
  • #5
Re: need help solving exponential problem

The question was this. A person is taking out a loan of $10,000, compounded monthly, with an interest rate of 2.14 percent. She is making payments of $230 / mo. How long before the loan is repaid?
 
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FAQ: Need help solving exponential problem

What is an exponential problem?

An exponential problem is a mathematical problem that involves an unknown quantity being raised to a power, such as 2x or 10n. These problems often involve growth or decay over time and are commonly used in science and finance.

How do I solve an exponential problem?

To solve an exponential problem, you can use logarithms or write the problem in its equivalent form, such as 2x = 8 as x = log28. You can also use a calculator or online tool to solve these problems.

What are some common applications of exponential problems?

Exponential problems are commonly used in science to model growth and decay of populations, as well as in finance to calculate compound interest. They are also used in physics and engineering to model exponential growth and decay in natural phenomena.

What is the difference between exponential and logarithmic functions?

An exponential function is a function in which the independent variable is the exponent, while a logarithmic function is a function in which the independent variable is the exponent's base. In other words, exponential functions involve raising a number to a power, while logarithmic functions involve taking the logarithm of a number.

What are some strategies for solving difficult exponential problems?

Some strategies for solving difficult exponential problems include using the properties of logarithms, factoring, and substitution. It can also be helpful to break the problem down into smaller parts and work through each part systematically. Additionally, practicing with different types of exponential problems can help develop problem-solving skills.

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