Identify the initial amount a and the decay factor b in each exponential function.
1.) y= 0.1* 0.9^x
well, since they are usually written as
y = a * b^x
it seems pretty clear, wouldn't you say?
In the exponential function y = 0.1 * 0.9^x, we can identify the initial amount (a) as 0.1 and the decay factor (b) as 0.9.
To identify the initial amount (a) and the decay factor (b) in the exponential function, we need to look at the general form of an exponential function:
y = a * b^x
In the given function, y = 0.1 * 0.9^x, we can determine the values of a and b.
1.) Initial amount (a):
The initial amount is the value of y when x = 0. So let's substitute x = 0 into the function:
y = 0.1 * 0.9^0
Any number, except 0, to the power of 0 is equal to 1. Therefore:
y = 0.1 * 1
y = 0.1
So, the initial amount (a) in this function is 0.1.
2.) Decay factor (b):
The decay factor is the base of the exponential function, which determines how the function decreases or decays. In this case, the decay factor is 0.9.
Therefore, in the function y = 0.1 * 0.9^x, the initial amount (a) is 0.1, and the decay factor (b) is 0.9.