0. Functions

Common Functions

0. Functions

Common Functions

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Multiple Choice

Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=3\left(1.5\right)^{x}$

Exponential function, $f\left(4\right)=410.06$

Exponential function, $f\left(4\right)=15.19$

Not an exponential function

Verified step by step guidance

Step 1: Understand the definition of an exponential function. An exponential function is of the form f(x) = a * b^x, where 'a' is a constant (the initial value), 'b' is the base (a positive constant), and 'x' is the exponent (a variable).

Step 2: Analyze the given function f(x) = 3(1.5)^x. Here, the constant 'a' is 3, the base 'b' is 1.5, and the exponent is the variable 'x'. This matches the form of an exponential function.

Step 3: Identify the base and the power. In this case, the base is 1.5, and the power is the variable 'x'.

Step 4: To evaluate the function at x = 4, substitute x = 4 into the function: f(4) = 3(1.5)^4. This means you will calculate 1.5 raised to the power of 4 and then multiply the result by 3.

Step 5: Perform the calculation step-by-step: First, compute 1.5^4, then multiply the result by 3 to find f(4). This will give you the value of the function at x = 4.