Question

For the following functions, identify whether they are growth or decay *3 pointsA) y = (2)^x +3B) y = (1/3)^x - 1C) y = (0.5)^x

Answer 1

The exponential function

The general form of the exponential function is:

`f(x)=a\cdot b^x+c`

Where b is the ratio of growth or decay of the function.

The function can be identified as a growing or decaying trend according to:

* If b is greater than 1, the function is growing

* If b is less than 1, the function is decaying.

Now let's analyze the given functions:

A)

`y=2^x+3`

The ratio of this function is b=2, thus the function is growth.

B)

`y=((1)/(3))^x-1`

Here, the value of b is 1/3 and it's less than 1, thus the function is decay.

C)

`y=(0.5)^x^{}`

Here, the value of b is 0.5 and it's less than 1, thus the function is decay

Answer:

A) Growth

B) Decay

C) Decay