Show work and explain.[tex]10) \: y = 10({.5})^{x} [/tex]Growth or Decay?y-intercept?Domain:Range:
Accepted Solution
A:
Answer: Decay, y-intercept = 10, D: x is All Real Numbers, R: y > 0Step-by-step explanation:y = 10(0.5)ˣ ↓ represents the y-intercept (when x = 0, y = 10(0.5)⁰ = 10)y = 10(0.5)ˣ ↓ If >1, represents growth. If <1, represents decay.Domain: There are no restrictions on x so x is All Real Numbers (-∞, ∞)Range: No matter what value x is, y has to be greater than 0 (0, ∞)We can also show this algebraically: y = 10(0.5)ˣlog y = log 10(0.5)ˣ ↓ y > 0 because you cannot take the log of 0 or a negative valueSee graph