Question

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

Answer 1

Answer: $y=\frac{5}{9}$

Step-by-step 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 $b \neq 1$ , "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:

$a^{-n}=\frac{1}{a^n}$

Then:

$y=\frac{15}{3^{3}}$

2. Simplifying, you get:

$y=\frac{15}{27}\\\\y=\frac{5}{9}$