Answer:
y = [tex]15(4)^{x} [/tex] or y = [tex] 15(-4)^{x} [/tex]
Step-by-step explanation:
Standard equation is: y= [tex] ab^{x}[/tex] ................(1)
The function passes through (0,15) and (2,240).
so, by putting x = 0 and y = 15, we get
15 = [tex] ab^{0} [/tex]
a = 15
Also, putting x= 2 and y= 240, we get
240 = [tex] ab^{2} [/tex]
240 = [tex] 15b^{2} [/tex]
[tex] b^{2} [/tex] = [tex]\frac{240}{15}[/tex]
[tex] b^{2} [/tex] = 14
b = 4 or b= -4
Putting the values of a and b in (1), we get
y = [tex]15(4)^{x} [/tex] or y = [tex] 15(-4)^{x} [/tex]
