University:
Augusta University
Course:
MATH 4800 | Secondary Mathematics from an Advanced Perspective
Academic year:

2024
Views:

378

Pages:

2
Author:

Autumn Cox

Question 1 When does the function y = ab^x represent exponential growth? exponential decay? Answer The function y = ab^x represents exponential: 1- GROWTH b=1+r and r>0 2- DECAY b=1-r and 0 < b < 1 Question 2 To model each circumstance, create an exponential growth or decay function. After the specified amount of time, determine the function's value. A new car costs $25,000, yet after six years, it loses 15% of its value. Answer y = a(1 - r)^t y = 25000(1 - 0.15)^t t=6 y = 25000(1 – 0.15)^6 y = 9428.74 Question 3 State whether the equation represents exponential growth, exponential decay, or neither. y = 0.82 * 3^x Answer The exponential function: y = a * b^x is an exponential growth if b > 1 or is an exponential decay if 0 < b < 1. Here, b = 3 so it is an EXPONENTIAL GROWTH. Question 4 Determine whether the function represents exponential growth or exponential decay. f(x) = 50(1.1^x)^2 Answer Use the Power of a Power Rule to have: f(x) = 50 * (1.1^2)^x Evaluate the power to have: f(x) = 50 * (1.21)^x The base of the function is 1.21 which is greater than 1. This means that the function involves an exponential growth. Question 5 Find the multiplier for the rate of exponential growth or decay. 1% decay Answer The decay rate multiplier for 1% decay is: r=1-1% Write the percentage as a decimal r=1-0.01 Subtract r=0.99