Question

Given the function f(x)=28(1.5)^x, evaluate each of the following. Round answers to the nearest hundredth as needed. f(−3)= f(−2)= f(−1)=

Answer 1

Based on the given exponential function, the output values include;

f(-3) = 8.30

f(-2) = 12.44

f(-1) = 18.67

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

`f(x)=a(b)^x`

Where:

• a represents the initial value or y-intercept.
• x represents x-variable.
• b represents the rate of change or common ratio.

Next, we would determine each of the output values by substituting the respective input value into the given exponential function as follows;

`f(x)=28(1.5)^x\\\\f(-3)=28(1.5)^(-3)\\\\f(-3)=8.30\\\\\\\\f(--2)=28(1.5)^(-2)\\\\f(-2)=12.44\\\\\\\\f(-1)=28(1.5)^(-1)\\\\f(-1)=18.67`