Question 37·Easy·Nonlinear Functions

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The function $g$ is defined by $g(x) = k \cdot 4^{x}$ , where $k$ is a constant. If $g(1) = 12$ , what is the value of $k$ ?

In an exponential function like $g(x)=k\cdot b^x$ , the input goes in the exponent and $k$ is a fixed multiplier. A stated function value gives you both an input and an output: substitute the input, then set the result equal to the output. For one unknown constant, enter that equation in Desmos as a regression using $\sim$ . Don't mistake the base for the multiplier.

Hints

Hint 1
Function notation $g(1)$ means the output when the input is $1$ . Replace the $x$ in the exponent with $1$ . Which part of the rule is still unknown?
Hint 2
An exponent of $1$ leaves the base unchanged: $4^1=4$ . The given output must equal $4$ times the unknown multiplier. What equation can you enter with $\sim$ to find it?

Step-by-step

Substitute the input and fit the constant
Step 1
Turn the function value into an equation
In function notation, $g(1)$ means put $1$ in for $x$ . The given output is $12$ , so the input replaces the exponent's $x$ , not $k$ :
$12=k\cdot4^1.$
Step 2
Find the multiplier in Desmos
Type $12\sim k\cdot4^1$ as a regression: the tilde asks Desmos to find $k$ . Under PARAMETERS, Desmos reports $k=3$ . Since $4^1=4$ , this gives $g(1)=3\cdot4=12$ , so the requested constant is $3$ . Choice C.

Question 37·Easy·Nonlinear Functions

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