Question

Determine whether the equation is exponential growth or exponential decay

1a. y = 2(11/5)^-x

2b. y= e^-2x

3c. y= 1/4e^x​

Answer 1

9514 1404 393

Answer:

1. decay
2. decay
3. growth

Explanation:

If the base of a positive exponential is greater than 1, the function is a growth function. If it is less than 1, the function decays.

Remember that a^-1 = 1/a, so a negative exponential can be transformed to a positive one.

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1. y = 2(11/5)^-x = 2(5/11)^x . . . . 5/11 < 1, so decay

2. y = e^(-2x) = (1/e^2)^x . . . . 1/e^2 < 1, so decay

3. y = 1/4e^x . . . . e > 1, so growth

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e ≈ 2.71828 . . . an irrational number