We appreciate your visit to Given tex a 97 tex tex r 60 tex What is the exponential decay function A tex f x 97 0 4 x tex B. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To write an exponential decay function given the initial amount and the decay rate, you can follow these steps:
1. Understand the terms:
- [tex]\( a \)[/tex] is the initial amount. In this case, it's given as 97.
- [tex]\( r \)[/tex] is the rate of decay. Here, it's 60%, which needs to be converted into decimal form for calculation. So, [tex]\( r = \frac{60}{100} = 0.6 \)[/tex].
2. Use the exponential decay formula:
- The standard formula for exponential decay is:
[tex]\[
f(x) = a \times (1 - r)^x
\][/tex]
- In this formula:
- [tex]\( a \)[/tex] is the initial amount.
- [tex]\( 1 - r \)[/tex] is the base of the exponential function. It represents the remaining percentage after decay.
3. Substitute the values:
- Substitute the given [tex]\( a \)[/tex] and [tex]\( r \)[/tex] into the formula:
[tex]\[
f(x) = 97 \times (1 - 0.6)^x
\][/tex]
4. Calculate the base:
- Compute [tex]\( 1 - 0.6 \)[/tex], which gives you 0.4. This means that 40% of the quantity remains after each step of decay.
5. Write the final exponential decay function:
- Therefore, the exponential decay function is:
[tex]\[
f(x) = 97 \times (0.4)^x
\][/tex]
This function models the decay process starting at 97 and decreasing by 60% with each successive step (or time period). Thus, the correct choice from the options provided is [tex]\( f(x) = 97(0.4)^x \)[/tex].
1. Understand the terms:
- [tex]\( a \)[/tex] is the initial amount. In this case, it's given as 97.
- [tex]\( r \)[/tex] is the rate of decay. Here, it's 60%, which needs to be converted into decimal form for calculation. So, [tex]\( r = \frac{60}{100} = 0.6 \)[/tex].
2. Use the exponential decay formula:
- The standard formula for exponential decay is:
[tex]\[
f(x) = a \times (1 - r)^x
\][/tex]
- In this formula:
- [tex]\( a \)[/tex] is the initial amount.
- [tex]\( 1 - r \)[/tex] is the base of the exponential function. It represents the remaining percentage after decay.
3. Substitute the values:
- Substitute the given [tex]\( a \)[/tex] and [tex]\( r \)[/tex] into the formula:
[tex]\[
f(x) = 97 \times (1 - 0.6)^x
\][/tex]
4. Calculate the base:
- Compute [tex]\( 1 - 0.6 \)[/tex], which gives you 0.4. This means that 40% of the quantity remains after each step of decay.
5. Write the final exponential decay function:
- Therefore, the exponential decay function is:
[tex]\[
f(x) = 97 \times (0.4)^x
\][/tex]
This function models the decay process starting at 97 and decreasing by 60% with each successive step (or time period). Thus, the correct choice from the options provided is [tex]\( f(x) = 97(0.4)^x \)[/tex].
Thanks for taking the time to read Given tex a 97 tex tex r 60 tex What is the exponential decay function A tex f x 97 0 4 x tex B. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
