SOLUTION: Hi, I need help with solving this exponential functions it says what are the key features of y=-3(1/4)^x increasing or decreasing, Y-int?, Common Ratio, and Horizontal Asymptote. A

Algebra ->  Functions -> SOLUTION: Hi, I need help with solving this exponential functions it says what are the key features of y=-3(1/4)^x increasing or decreasing, Y-int?, Common Ratio, and Horizontal Asymptote. A      Log On


   

Question 1150223: Hi, I need help with solving this exponential functions it says what are the key features of y=-3(1/4)^x increasing or decreasing, Y-int?, Common Ratio, and Horizontal Asymptote. And what would happen if the equation was -3(1/4)^x-2
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
y = -3 * (1/4) ^ x is increasing.

the y-intercept occurs when x = 0.

that would be when y = -3 * (1/4) ^ 0 which becomes y = -3.

the common ratio is 1/4 because each time x is increased by 1, the current value is multiplied by 1/4.

the horizontal asymptote is 0 because (1/4) ^ x is equal to (1 ^ x) / (4 ^ x) which is equal to 1 / (4 ^ x).
the numerator stays the same and the denominator gets larger and larger, so the fraction approaches 0 but is never equal to 0.
-3 * 0 = 0

if the equation was -3 * (1/4) ^ x - 2, then the y-intercept would become -5 and the horizontal asymptote would become - 2.

here's what the graph looks like for both y = -3 * (1/4) ^ x and y = -3 * (1/4) ^ x - 2

y = -3 * (1/4) ^ x is in red.
y = -3 * (1/4) ^ x - 2 is in blue.

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