Identify each function as modeling either exponential growth

Answered question

2022-04-07

 Identify each function as modeling either exponential growth or exponential decay . What percent of increase or decrease does the function model ? 2. y = 0.32 * (0.99) ^ x 3. y = 0.1 * (1.7) ^ x 4. y = 7.3 * (0.8) ^ x; y = 15 * (1.45) ^ x

Answer & Explanation

alenahelenash

alenahelenash

Expert2023-04-27Added 556 answers

Let's first recall the formulas for exponential growth and decay functions:
Exponential Growth: y=a·bx where b>1
Exponential Decay: y=a·bx where 0<b<1
In both formulas, a represents the initial amount, and b represents the growth or decay factor.
Now, let's identify each function as modeling either exponential growth or exponential decay:
2. y=0.32·(0.99)x
This is an example of exponential decay since 0<0.99<1. The decay factor is b=0.99. To find the percentage of decrease, we can use the formula:
Percentage of decrease = |1b|·100
Thus, the percentage of decrease for this function is:
|10.99|·1001%
Therefore, the function models exponential decay with a decrease of approximately 1%.
3. y=0.1·(1.7)x
This is an example of exponential growth since 1.7>1. The growth factor is b=1.7. To find the percentage of increase, we can use the formula:
Percentage of increase = (b1)·100
Thus, the percentage of increase for this function is:
(1.71)·100=70%
Therefore, the function models exponential growth with an increase of 70%.
4. y=7.3·(0.8)x;y=15·(1.45)x
Both of these functions are examples of exponential decay and growth respectively, with decay factor b=0.8 and growth factor b=1.45. Using the same formulas as above, we can find the percentages of decrease and increase:
Percentage of decrease for the first function:
|10.8|·100=20%
Percentage of increase for the second function:
(1.451)·100=45%
Therefore, the first function models exponential decay with a decrease of 20%, and the second function models exponential growth with an increase of 45%.

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