Question

use the graph of the exponential growth function $f(x) = a(2^x)$ to determine which statement is true. $f(0) = 2$ when $a = \frac{1}{2}$. $f(0) = 3$ when $a = 3$. $f(1) = 9$ when $a = 9$.

Explanation:

Step1: Recall the function formula

The function is \( f(x) = a(2^x) \). We need to evaluate \( f(0) \) or \( f(1) \) for given \( a \) values.

Step2: Evaluate \( f(0) \) for a general \( a \)

Substitute \( x = 0 \) into \( f(x) \): \( f(0) = a(2^0) = a(1) = a \).

Step3: Check each statement

• For " \( f(0) = 2 \) when \( a = \frac{1}{2} \)": From Step2, \( f(0) = a \), so if \( a = \frac{1}{2} \), \( f(0) = \frac{1}{2}

eq 2 \). False.

• For " \( f(0) = 3 \) when \( a = 3 \)": From Step2, \( f(0) = a \), so if \( a = 3 \), \( f(0) = 3 \). True.
• For " \( f(1) = 9 \) when \( a = 9 \)": Substitute \( x = 1 \), \( f(1) = 9(2^1) = 18

eq 9 \). False.

Answer:

\( f(0) = 3 \) when \( a = 3 \) (the second statement)