identify the initial amount in the following exponential function y=2.3(1.32)x
We write exponents in this fashion.
y=2.3(1.32)^x
"initial" means at the beginning, or mathematically when x = 0
y = 2.3(1.32)^0
= 2.3(1) = ....
In the exponential function y = 2.3(1.32)^x, the initial amount can be identified as the coefficient of the base, which is (1.32)^0.
Since any number raised to the power of 0 is equal to 1, the initial amount in this exponential function is 2.3.
To identify the initial amount in the exponential function y = 2.3(1.32)^x, we can utilize the concept of exponential growth or decay.
The general form of an exponential function is: y = a * b^x, where:
- "a" represents the initial amount or starting value,
- "b" represents the growth or decay factor, and
- "x" represents the exponent or the number of times the growth or decay occurs.
In this case, the given function is y = 2.3(1.32)^x. Notice that the coefficient in front of the parentheses is 2.3. This number represents the initial amount or starting value of the function. Therefore, the initial amount in this exponential function is 2.3.
To clarify, if x = 0, the exponential term (1.32)^0 equals 1, and multiplying the initial value of 2.3 by 1 results in the initial amount remaining unchanged. Hence, 2.3 is the initial amount in the given exponential function.