Answer:
[tex]y=150*3^{x}[/tex]
Step-by-step explanation:
so basically make a system of equations using what's given and solve.
Understand that the equation is the same as [tex]y=ab^{x}[/tex]
First: make two points to plug in
(0, 150) and (1, 450)
Therefore x (or t) is the time in months
and y (or N) is the number of lilies
Second: Plug in to make system
[tex]150=ab^{0} \\450=ab^{1}[/tex]
Third: solve
let's start with the fist equation
first simplify: b to the zero power is just 1 [tex]b^{0} =1[/tex]
[tex]150=a1\\150=a[/tex]
Now plug in 150 to the a in the other equation
[tex]450=ab^{1}\\450=150b^{1}[/tex]
solve for b
simplify: [tex]b^{1} =b[/tex]
[tex]450=150b[/tex]
b=3
now you're done
equation: [tex]y=150*3^{x}[/tex]
