Interpreting Parts of Exponentials in Context EOC Review: Interpreting Parts of Exponentials in Context

initial value (y-intercept) rate of change EXPONENTIAL FUNCTION y = a(b)x initial value (y-intercept) rate of change

initial value (y-intercept) rate of change GROWTH & DECAY y = a(1± r)x initial value (y-intercept) rate of change + growth (more than 1.00) - decay (less than 1.00)

Example: E#3.1 How do we know it is exponential? Where do we find the percent rate of change? How do we know it is growth or decay? The function f(x) = 20,000(1.08)x models the population of a town where x is the number of years since 2005. Which statement is true about the population of the town? A. The population of the town is decreasing at a rate of 12% per year. B. The population of the town is decreasing at a rate of 8% per year. C. The population of the town is increasing at a rate of 12% per year. D. The population of the town is increasing at a rate of 8% per year.

Example E#3.2 How do we know this is exponential? The size of a population of a town can be modeled by the function P = 20,000(1.08)x, where x is the number of years since 2005. What does 20,000 represent in this function? Is the 20,000 the y-intercept or the percent rate of change?

You Try! Examine the parts of the function. Ask: What is the initial value? Is the rate growth or decay?

Check it E#3.3 A fungus is growing in a petri dish. The fungi count for t days since the lab started is modeled by the function f(x) = 4(1.2)t . At what rate is the population increasing each day?

Check it: E#3.4 The function f(t) = 500(0.8)t models the size of a population of fish in a pond t years after it was first stocked in 2015. What does 500 represent in this function?

Check it: E#3.5 Animal control estimated that there is a population of feral cats150 growing at a rate of 15% per year, t. Write an equation models the population of cats over the years?

Check it E#3.6 The equation y = 550(1.05)x models the value of an investment after x years. Which statement is true about the value of the investment? A. The value of the investment is growing by $550 each year. B. The value of the investment is growing by 5% each year. C. The value of the investment is decreasing by $550 each year. D. The value of the investment is decreasing by 5% each year.