Question 185·Medium·Nonlinear Functions
The table shows several values of and their corresponding values of for the function .
| 2 | 3 |
| 3 | 17 |
| 4 |
In the table, is a constant. What is the value of ?
For function-table questions, first recognize that a missing table entry like c is just the function evaluated at that x-value (here, ). Substitute the given x into the formula, simplify the exponent before computing the power, then multiply and apply any added or subtracted constants at the end. Work step by step to avoid common mistakes like dropping a final term or misreading the exponent.
Hints
Connect c to the function
Look at the table: what input of corresponds to ? How can you write in terms of ?
Use the given formula directly
You are given . Substitute the appropriate -value from the row with into this formula.
Simplify carefully, step by step
After substituting, first simplify the exponent , then compute the power of 3, then multiply by 7, and only at the end apply the .
Desmos Guide
Enter the function
In Desmos, type f(x) = 7*3^(x-2) - 4 so the calculator stores the function .
Evaluate the function at x = 4
In a new line, type f(4) (or create a table for and enter in the -column). The value that Desmos gives for is the constant in the table.
Step-by-step Explanation
Identify what c represents
From the table, the value is the output of the function when . In other words, for the function
So the problem is asking you to compute .
Substitute x = 4 into the function
Replace with in the expression for :
Now simplify the exponent first, before dealing with the power or multiplication.
Simplify the exponent and power
Compute the exponent:
so the expression becomes
Now evaluate :
so we have
Finish the arithmetic to find c
Multiply first:
Now subtract :
Since , the value of is 59.