Question

What is the multiplicative rate of change for the exponential function f(x)=2 (5/2)-x

Answer 1

f(x)=2(5/2)-x
y(0,2)
Is the intercept
Dom:x->IR

Answer 2

The multiplicative rate of change is
`(2)/(5)`

Explanation:

Here, the given function,

`f(x)=2((5)/(2))^(-x)`

`=2((5^(-x))/(2^(-x))`

`=2((2^x)/(5^x)`

`\implies f(x)=2((2)/(5))^x`

Which is an exponential function,

Since, in an exponential function
`f(x)=ab^x`

b is called growth factor or multiplicative rate of change,

By comparing,

b = 2/5,

Hence, The multiplicative rate of change of the given function is
`(2)/(5)`