Question

Evaluate the function rule for the given value. y=15*3^x for x = -3

Answer 1

Answer:
`y=(5)/(9)`

Explanation:

It is important to remember that an Exponential function has the following form:

`f(x) =a* b^x`

Where “b” is
`b > 0` and
`b \\eq 1` , "a" is a coefficient, "x" is the Independent variable and f(x) is the Dependent variable.

In this case, you have the following Exponential Function given in the exercise:

`y=15*3^x`

If the value of Dependent variable is -3, then:

`x=-3`

So, you must substitute that value of "x" into the function:

`y=15*3^((-3))`

And now you must evaluate:

1. According the Negative exponent rule:

`a^(-n)=(1)/(a^n)`

Then:

`y=(15)/(3^(3))`

2. Simplifying, you get:

`y=(15)/(27)\\\\y=(5)/(9)`