Answer:
[tex]y = 18 \times {7}^{x} [/tex]
Step-by-step explanation:
Using the formula for exponential function,
[tex]y = ab {}^{x} [/tex]
Let plug in 0,18.
[tex]18 = ab {}^{0} [/tex]
Using the zero power rule,
[tex]b {}^{0} = 1[/tex]
[tex]18 = a \times 1[/tex]
[tex]a = 18[/tex]
Since a equal 18 let plug in what we know so far
[tex]y = {18b}^{x} [/tex]
Now let find b.
Let use the other point, 3,6174
[tex]6174 = {18b}^{3} [/tex]
Divide 18 by both sides and we get
[tex]343 = b {}^{3} [/tex]
Take the 3rd root of 343
[tex] \sqrt[3]{343} = b = 7[/tex]
b=7
The equation is
[tex]y = 18 \times 7 {}^{x} [/tex]
