Answer:
[tex] y = 6(2.5)^x [/tex]
Step-by-step explanation:
[tex] y = ab^x [/tex]
Use (0, 6) and solve for a:
[tex] 6 = ab^0 [/tex]
[tex] 6 = a \times 1 [/tex]
[tex] a = 6 [/tex]
Use a = 6 and (1, 15) and solve for b.
[tex] 15 = 6b^1 [/tex]
[tex] 15 = 6b [/tex]
[tex] 6 = 2.5 [/tex]
[tex] y = 6(2.5)^x [/tex]
Answer:
see explanation
Step-by-step explanation:
Obtain the exponential function by substituting the given points into the equation.
Equation in form
y = a [tex]b^{x}[/tex]
Using (0, 6), then
6 = a [tex]b^{0}[/tex] = a ⇒ a = 6
Using (1, 15), then
15 = 6 [tex]b^{1}[/tex] = 6b ( divide both sides by 6 )
[tex]\frac{15}{6}[/tex] = b, hence
b = [tex]\frac{5}{2}[/tex]
Exponential equation is y = 6 [tex](\frac{5}{2}) ^{x}[/tex]
