Answer:
[tex]y = 5(6) {}^{x} [/tex]
Step-by-step explanation:
A exponential function is represented by
[tex]y = ab {}^{x} [/tex]
where a is the vertical stretch and b is the base and x is the nth
power of x
Since the first number corresponds with zero, that means our y intercept is the first number.
This means when x=0 , y=5 so let find the value of 5.
[tex]5 = ab {}^{0} [/tex]
b to the 0th power equal 1 so
[tex]5 = a \times 1[/tex]
[tex]a = 5[/tex]
Our equation is for now
[tex]y = 5b {}^{x} [/tex]
Now let plug in 1,30
[tex]30 = 5b {}^{1} [/tex]
Divide 5 by both sides
[tex]6 = b {}^{1} [/tex]
Anything to the 1st power is itself so b equal 6.
So our equation is
[tex]y = 5(6) {}^{x} [/tex]
