Respuesta :

tramserran

Answer:  Decay, y-intercept = 10, D: x is All Real Numbers, R: y > 0

Step-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)ˣ

log y = log 10(0.5)ˣ

     ↓

    y > 0   because you cannot take the log of 0 or a negative value

See graph

Ver imagen tramserran
gmany

Step-by-step explanation:

[tex]y=b(a)^x\\\\\text{If}\ 0<a<1,\ \text{then decay}.\\\text{If}\ a>1,\ \text{then growth.}\\\\\text{We have}\ y=10(0.5)^x\to a=0.5<1.\ \text{Therefore:}\boxed{DECAY}}\\\\y-intercept\ \text{is for x = 0. Substitute:}\\\\y=10(0.5)^0=10(1)=10\to\boxed{y-intercept=10}\\\\Domain:\text{ We can substitute any number for x,}\\\text{ because the number 0.5 can be up to any power.}\\\\\boxed{Domain=\mathbb{R}}-\text{the set of all real numbers}[/tex]

[tex]Range:\\\text{Calculate the limits of a function:}\\\\\lim\limits_{x\to-\infty}10(0.5)^x=10\lim\limits_{x\to-\infty}\left(\dfrac{1}{2}\right)^x=10\lim\limits_{x\to-\infty}2^{-x}=10(\infty)=\infty\\\\\lim\limits_{x\to\infty}10(0.5)^x=10\lim\limits_{x\to\infty}\left(\dfrac{1}{2}\right)^x=10(0)=0\\\\\boxed{Range=(0,\ \infty)}[/tex]

Ver imagen gmany

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