Answer:
a = 8, b = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given the exponential function
f(x) = a[tex]b^{x}[/tex]
To find a and b use the given coordinate points on the graph
Using (0, 8 ), then
8 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then
a = 8
f(x) = 8[tex]b^{x}[/tex]
Using (2, 18 ) , then
18 = 8b² ( divide both sides by 8 )
[tex]\frac{18}{8}[/tex] = b² , that is
b² = [tex]\frac{9}{4}[/tex] ( take the square root of both sides )
b = [tex]\sqrt{\frac{9}{4} }[/tex] = [tex]\frac{3}{2}[/tex]
Thus
f(x) = 8[tex](\frac{3}{2}) ^{x}[/tex]
