7­6 Exponential Functions exponential​
(adjective) ek spoh NEN shul Related Word:​
exponent (noun) Main Idea:​
You can use exponential notation to write a repeated multiplication (such as 8 × 8 × 8 × 8 ) using a base and an exponent ( 84 ). An exponential function has a variable as an exponent. Essential Understanding​
Some functions model an initial amount that is repeatedly multiplied by the same positive number. In the rules for these functions, the independent variable is an exponent. Suppose all the x­values in a table have a common difference. If all the y­values have a common difference, then the table represents a linear function. If all the y­values have a common ratio, then the table represents an exponential function. Determine whether each table or rule represents a linear or an exponential function. Explain why or why not. A.) B.) y = 12 • x C.) y = 7x + 3 Evaluate each function for the given value. D.) g (t) = 2 • 0.4t for t =− 2 E.) h (w) =− 0.5 • 4w for w = 18 F.) ​
Wildlife Management​
A population of 75 foxes in a wildlife preserve quadruples in size every 15 yr. The function y = 75 • 4x , where x is the number of 15­yr. periods, models the population growth. How many foxes will there be after 45 yr? Graph each exponential Function. x
G.) y =− 4x
H.) y =− ( 13 ) I.) y = 0.1 • 2x
J.) y = 1.25x