Is my answer correct? (Exponential Functions)

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In summary, there are different methods for solving exponential functions, such as using logarithms, graphing, and properties of exponents. To check if your answer is correct, you can plug it into the original equation or use a calculator. Common mistakes to avoid include incorrect application of properties of exponents and calculation errors. Special cases and exceptions may arise when the base of the exponent is negative or when the exponent is a fraction. Calculators can be used to solve exponential function problems, but it's important to understand the steps and concepts behind the solution.
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tardisblue
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13) The temperature of a cup of coffee can be approximated by the equation \(\displaystyle T(t) = P(\frac{441}{450})^t\), where T is the temperature in Celsius, t is time in minutes and P is the initial temperature of the coffee. If the initial temperature of the coffee is 102 degrees celsius, when will the coffee be 60 degrees celsius?

So, my answer was that the coffee will be 60 degrees celsius after 26.4 minutes. Is this correct? I can show my work if it's wrong. Thanks.
 
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  • #2
WolframAlpha says the answer is $t=26.265$, which is pretty close to your answer.
 

FAQ: Is my answer correct? (Exponential Functions)

1. Is there a specific way to solve exponential function problems?

Yes, there are different methods for solving exponential functions depending on the type of problem. Some common methods include using logarithms, graphing, and using properties of exponents.

2. How do I know if my answer for an exponential function problem is correct?

You can check your answer by plugging it back into the original equation and seeing if it satisfies the equation. You can also use a calculator or graphing software to confirm your answer.

3. What are the common mistakes to avoid when solving exponential function problems?

Sometimes people forget to apply the properties of exponents correctly, or they may accidentally make a calculation error. It's important to double-check your work and be familiar with the rules for solving exponential functions.

4. Are there any special cases or exceptions when solving exponential function problems?

Yes, there are special cases such as when the base of the exponent is negative or when the exponent is a fraction. In these cases, different rules and methods may need to be applied.

5. Can I use a calculator to solve exponential function problems?

Yes, you can use a calculator to solve exponential function problems. However, it's important to understand the steps and concepts behind solving these problems in case you encounter a similar problem without a calculator.

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