Identify the initial value and growth or decay factor in each of the following exponential functions:
a) y= 350 x 5^x
b) Q= 25000 x (1/2)^t
c) P=(7 x 10^3) x 4^t
d) N= 5000 x (9/10)^t
in general if the base of the exponential factor is less than 1, you will have decay, if the base is greater than 1, you will have growth.
To identify the initial value and growth or decay factor in each of the exponential functions, we can analyze the equation in the form y = a * b^x, where:
- "a" represents the initial value or starting amount,
- "b" represents the growth or decay factor.
a) In the equation y = 350 * 5^x:
- The initial value is the coefficient of the base, which is 350.
- The growth factor is the base of the exponential, which is 5.
b) In the equation Q = 25000 * (1/2)^t:
- The initial value is the coefficient of the base, which is 25000.
- The decay factor is the base of the exponential, which is 1/2. Since it is less than 1, it represents decay.
c) In the equation P = (7 x 10^3) * 4^t:
- The initial value is the coefficient of the base, which is (7 x 10^3), or 7000.
- The growth factor is the base of the exponential, which is 4.
d) In the equation N = 5000 * (9/10)^t:
- The initial value is the coefficient of the base, which is 5000.
- The decay factor is the base of the exponential, which is 9/10. Since it is less than 1, it represents decay.
Therefore, the initial value and growth or decay factor for each equation are as follows:
a) Initial Value: 350, Growth Factor: 5
b) Initial Value: 25000, Decay Factor: 1/2
c) Initial Value: 7000, Growth Factor: 4
d) Initial Value: 5000, Decay Factor: 9/10