Question

A "b" value of less than 1 produces a graph with exponential decay

Answer 1

If this statement is a True or False question.

Then, TRUE. A "b" value of less than 1 produces a graph with exponential decay.

We consider this formula: y = a*b^x or f(x) =a*b^x

a is the initial value, b is the rate, x is the exponent. 

If b has a value of less than 1, as the exponent increases the resulting value of y decreases.

f(x) = 20(0.90)^x

f(1) = 200(0.90)¹ = 180
f(2) = 200(0.90)² = 162
f(3) = 200(0.90)³ = 145.80
f(4) = 200(0.90)⁴ = 131.22
f(5) = 200(0.90)⁵ = 118.10

Exponential decay is the decrease in a quantity. As you can see in the given example the value of f(x) decreases as the value of x increases because the value of b is less than 1.