Answer: [tex]y=\frac{5}{9}[/tex]
Step-by-step explanation:
It is important to remember that an Exponential function has the following form:
[tex]f(x) =a* b^x[/tex]
Where “b” is [tex]b > 0[/tex] and [tex]b \neq 1[/tex] , "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:
[tex]y=15*3^x[/tex]
If the value of Dependent variable is -3, then:
[tex]x=-3[/tex]
So, you must substitute that value of "x" into the function:
[tex]y=15*3^{(-3)}[/tex]
And now you must evaluate:
1. According the Negative exponent rule:
[tex]a^{-n}=\frac{1}{a^n}[/tex]
Then:
[tex]y=\frac{15}{3^{3}}[/tex]
2. Simplifying, you get:
[tex]y=\frac{15}{27}\\\\y=\frac{5}{9}[/tex]
