Math Problem Statement

Find the missing value from the graph defining the function shown below. Note that the graph is not drawn to scale. f(x) = 6(1.5)^x, and you need to determine the value of f(1).

Solution

The question on the screen is asking for the missing value of f(x)f(x) when x=1x = 1 for the function f(x)=6(1.5)xf(x) = 6(1.5)^x.

To solve for f(1)f(1):

  1. Substitute x=1x = 1 into the function: f(1)=6(1.5)1f(1) = 6(1.5)^1

  2. Calculate (1.5)1(1.5)^1, which is simply 1.5: f(1)=6×1.5f(1) = 6 \times 1.5

  3. Multiply: f(1)=9f(1) = 9

Thus, the missing value at (1,?)(1, ?) is 9.

Would you like more details, or do you have any questions about this?


Here are some related questions for further practice:

  1. What would the value of f(2)f(2) be for this function?
  2. How would the function change if the base of the exponent was 2 instead of 1.5?
  3. Can you determine the initial value and growth rate from the function f(x)=6(1.5)xf(x) = 6(1.5)^x?
  4. What is the general formula for exponential growth functions?
  5. How would you graph an exponential function like f(x)=6(1.5)xf(x) = 6(1.5)^x?

Tip: For exponential functions, the base of the exponent (in this case, 1.5) determines if the function grows (if base > 1) or decays (if base < 1).

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Function Evaluation

Formulas

f(x) = a * b^x

Theorems

Properties of Exponential Functions

Suitable Grade Level

Grades 8-10