Question

Would these equations be either exponential decay or growth?

Y=3(2.01)^x-1.25
Y=-2.025(1/4)^x+3

Answer 1

Sub in a couple of values of x into both equations. Lets say x = 1, 2, 3. Notice that these values are increasing, and so x is increasing.
If we sub 1, 2, and 3 into the first equation, you'll notice that the answer gets bigger. It's an exponent to a number that's bigger than 1, and the exponent is not negative. Therefore, the number will increase so long as x increases. Thus, the first equation is exponential growth, as it grows with x.
Sub 1,2,3 into the second equation. The mulitiplier gets smaller, because it's an exponent of a fraction. The denominator gets smaller everytime that x increases, so that multiplier decreases. HOWEVER, the other multiplier is negative, and so you're making a negative smaller everytime that x increases. Thus, making a number more positive is exponential growth.