Answer:
B
Step-by-step explanation:
We can use the standard form of an exponential function:
[tex]y=a(b)^x[/tex]
The point (0, 18) tells us that y = 18 when x = 0. Hence:
[tex]\displaystyle 18=a(b)^0[/tex]
Simplify:
[tex]a=18[/tex]
Our equation is now:
[tex]\displaystyle y=18(b)^x[/tex]
Next, the point (-1, 15) tells us that y = 15 when x = -1. Hence:
[tex]15=18(b)^{-1}[/tex]
Isolate the variable:
[tex]\displaystyle \frac{1}{b}=\frac{5}{6}[/tex]
Hence:
[tex]\displaystyle b=\frac{6}{5}[/tex]
By substitution:
[tex]\displaystyle y=18\left(\frac{6}{5}\right)^x[/tex]
Our answer is B.
