Question

The price f(x), in dollars, of product A after x years is represented by the function below:

f(x) = 72(1.25)x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer.

Part B: The table below shows the price f(t), in dollars, of product B after t years:

t (number of years) 1 2 3 4
f(t) (price in dollars) 65 84.5 109.85 142.81


Which product recorded a greater percentage change in price over the previous year? Justify your answer.

Answer 1

part A) think about the base of the exponent (the number being raised to a power). if it's greater than 1. it's increasing, and if it's less than 1, it's decreasing.

for a increasing exponential function, the base is 1 + r where r is the growth rate as a decimal.
for a decreasing exponential function, the base is 1 - r where r is the rate of decrease as a decimal


so first off, determine whether your function is growing or decreasing. from there, determine r, and finally, multiply r by 100% to convert it to a percentage.

Answer 2

part B) assuming the growth rate is constant, take any price and subtract the previous price to find the amount it increased over 1 year. divide that by the lower price, then multiply by 100% to convert it to a percentage

for example, we can take year 1 and year 2's price. calculate 84.5 - 65 to find the amount of increase, then divide by 65, then multiply by 100%.