0. Functions

Exponential Functions

0. Functions

Exponential 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 not equal to 1), and 'x' is the exponent.

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

Step 3: Identify the base and the power. In this case, the base is b = 1.5, and the power is x. This confirms that the function is indeed an exponential function.

Step 4: To evaluate the function at x = 4, substitute x = 4 into the function. This gives f(4) = 3(1.5)^4. Use the rules of exponents to calculate (1.5)^4 and then multiply the result by 3.

Step 5: Simplify the expression to find the value of f(4). This involves calculating (1.5)^4 and then multiplying by 3. The final result will confirm the value of f(4).