Question

1. consider the curve $y = 5(2^x)$. 13a determine the $y$-intercept of the exponential curve. $y = 5$ 5 nailed it! 13b can the function value ever be negative? yes a no b

Explanation:

13b Solution:

Step1: Analyze the function \( y = 5(2^x) \)

The base of the exponential function \( 2^x \) is \( 2>0 \). For any real number \( x \), \( 2^x>0 \) (because an exponential function with a positive base and any real exponent is always positive).

Step2: Multiply by 5

We then multiply \( 2^x \) by 5. Since \( 2^x>0 \) and \( 5>0 \), the product \( 5\times2^x>0 \) for all real \( x \). So the function value \( y = 5(2^x) \) is always positive and can never be negative.

Answer:

B. No