Question

Identify the type of function represented by ?(x)=7.6).A. Exponential decayB. Decreasing linearC. Exponential growthD. Increasing linear

Answer 1

The function we have is:

`f(x)=7\cdot((1)/(2))^x^{}`

And we need to find which type of function this is.

First, let's find if this is an exponential function or a linear function.

Linear functions have the x-variable multiplied by a coefficient, and exponential functions have the x-variable as an exponent.

In this case, the function is exponential because the variable x is an exponent in the expression.

To choose between options A and C, we need to define if the function is an exponential decay or an exponential growth. To find this, we need to look at the number that has x as the exponent, in this case: 1/2. We define:

`a=(1)/(2)`

As a general rule of a number "a" has the exponent x, the function will be an exponential growth if a>1, and there will be an exponential decay is a is between 0 and 1 0

In this case, 1/2 is between 0 and 1, thus, the function is an exponential decay.

Answer: Exponential decay.