University:
Felician University
Course:
MATH-160 | College Algebra
Academic year:

2022
Views:

356

Pages:

3
Author:

Clint W.

Growth and Decay Day Notes Any quantity that grows or decays by a fixed percent at regular intervals is said to have exponential growth or exponential decay. General Form: y = a(b)^x Exponential Growth Functions y = a(b)^x When b > 1 and a > 0, the graph will be increasing (growing). Exponential Decay Functions y = a(b)^x When 0 < b < 1 and a > 0, the graph will be decreasing (decaying). EXAMPLES: Tell whether the following graphs represent an exponential growth or decay. A) Decay graph showing exponential decay As x → ∞, y → 0 As x → -∞, y → ∞ B) Growth graph showing exponential growth As x → ∞, y → ∞ As x → -∞, y → 0 B) Tell whether the following equations represent an exponential growth or decay. a. `y = 3(2)^x` Growth b. `y = 0.5(4)^x` Growth c. `y = (1/2)^x` Decay The general equation for an exponential GROWTH function is: y = a(1 + r)^x where, (1 + r) = b is the growth factor. The general equation for an exponential DECAY function is: y = a(1 - r)^x where, (1 - r) = b is the decay factor. (1 + r) is the growth factor and (1 - r) is the decay factor **More Examples:** Identify the initial value, the growth or decay factor, and the growth or decay rate of the exponential function. 1. y = 2.1(1.05)^x Growth or decay: Growth Initial value: 2.1 Growth or decay factor: 1.05 Growth or decay rate: 0.05 or 5% 2. y = 6(0.82)^x Growth or decay: Decay Initial value: 6 Growth or decay factor: 0.82 Growth or decay rate: -0.18 or -18% 3. | x | y | |---|---| | -1 | 0.5 | | 0 | 2 | | 1 | 8 | | 2 | 32 | | 3 | 128 | a) G/D Factor: 4 b) G/D Rate: 3 or 300% c) Initial Value: 2 d) Write Exponential Function: y = 2(4)^x 4. | x | y | | 0 | 16 | | 1 | 8 | | 2 | 4 | | 3 | 2 | | 4 | 1 | | 5 | 0.5 | | 6 | 0.25 | a) G/D Factor: 1/2 or 0.5 b) G/D Rate: -1/2 or -50% c) Initial Value: 16 d) Exponential Function: y = 16(1/2)^x 7. The Johnson Company calculates the value of its stock each year by using the function y = 120(0.98)^x. Growth or decay: Decay Initial value: 120 Growth or decay factor: 0.98 Growth or decay rate: -0.02 or -2% 8. Selena's starting salary for her new marketing management job is $32,000. She calculates her projected salary for the next 5 years by using the function y = 32,000(1.12)^x. Growth or decay: Growth Initial value: 32,000 Growth or decay factor: 1.12 Growth or decay rate: 0.12 or 12%