WRITE EXPONENTIAL FUNCTIONS AND CONSTANT RATIOS Constant Ratio

WRITE EXPONENTIAL FUNCTIONS AND CONSTANT RATIOS

Constant Ratio / Common Ratio ◦ Remember that in a geometric sequence the terms have a constant ratio (common ratio / constant multiplier). ◦ Each term is multiplied by the same value to create the next term ◦ Example: 4, 12, 36, 108, … ◦ the constant ratio is 3 because each term is multiplied by 3 to make the next term ◦ Example: 9, 3, 1, 1/3, … ◦ the constant ratio is 1/3 because each term is multiplied by 1/3 to make the next term (like dividing by 3) ◦ This makes an exponential function (only if the constant ratio is positive) ◦ To identify a constant ratio, divide a term by the preceding (previous) term. If the ratio between all terms is the same (constant) it is an exponential function.

Write Exponential Functions ◦ Exponential Functions use form f(x)=abx ◦ a is the y-intercept (0, a) ◦ b is the common ratio ◦ First identify the constant ratio by comparing y output values from a table or graph (if it is hard to spot the constant ratio mentally, set up a division problem) ◦ Second identify the y-intercept ◦ Write in f(x)=abx form

Write Exponential Functions from Tables To find the constant ratio: divide one term by the previous term. That ratio should match for all y values 5 10 -6 = 3 -2 5 -18 = 3 -6

Write Exponential Functions from Tables To find the constant ratio: divide one term by the previous term. That ratio should match for all y values 2 3 2 To find the constant ratio: divide one term by the previous term. That ratio should match for all y values 15 9

Write Exponential Functions from Graphs To find the constant ratio: divide one term by the previous term. That ratio should match for all y values 9 6 = 1. 5 6 =3 2 Constant ratio: 3 y-intercept: 2 Exponential function: g(x)=2(3)x Constant ratio: 1. 5 y-intercept: 6 Exponential function: g(x)=6(1. 5)x -5 =5 -1 Constant ratio: 5 y-intercept: -1 Exponential function: g(x)=-1(5)x