Answer:
y = 8(50)^t : growth
y = 8(0.50)^t : decay
Explanation:
Whether the exponential function represents growth or decay depends on the magnitude of the base and the sign of the variable in the exponent.
Exponential functions
In general, an exponential function will be of the form ...
y = a·b^x
where 'a' is a scale factor (or "initial value") and 'b' is the base. Any scale factor or translation associated with the variable x can be used to alter the values of 'a' and 'b' appropriately to put the function in this form.
For example, y = a·b^(x+3) = (a·b^3)(b^x).
Similarly, y = a·b^(-x) = a·(1/b)^x
Growth
When the value of 'b' is greater than 1, increasing x will increase the value of y. This is the characteristic of a growth function.
Decay
When the value of 'b' is less than 1, increasing x will decrease the value of y. This makes it a decay function.
Application
Your function y = 8·50^t has a base of 50, which is greater than 1.
It is a growth function.
On the other hand, y = 8·0.50^t has a base of 0.50, which is less than 1. That function is a decay function.
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Additional comment
For real values of x and y, we generally require 0 < b. The base can be negative if the domain of the exponent is restricted to integers, or fractions with an odd integer denominator.