Respuesta :
Answer:
A) The graph passes through the point (0, 3), and for each increase of 1 in the x-values, the y-values increase by 1.8
Step-by-step explanation:
We are given the function, [tex]f(x) = 3(1.8)^x[/tex].
First, we will substitute x= 0 in the function.
So, we get,
[tex]f(x) = 3(1.8)^x[/tex] implies [tex]f(0) = 3(1.8)^0[/tex] i.e. f(0)= 3
Thus, the graph of the function passes through the point (0,3).
Also, we get the table of the values as,
x [tex]f(x) = 3(1.8)^x[/tex] Difference in f(x) values
1 [tex]f(1) = 3(1.8)^1= 5.4[/tex] 9.72-5.4 = 4.32
2 [tex]f(2) = 3(1.8)^2= 9.72[/tex] 17.496 -9.72= 7.776
3 [tex]f(3) = 3(1.8)^3= 17.496[/tex] 1.4928-17.496=13.997
4 [tex]f(3) = 3(1.8)^4= 31.4928[/tex]
As, we have,
The factor of increase in the y-values = [tex]\frac{7.776}{4.32}[/tex] = [tex]\frac{13.997}{7.776}[/tex] = 1.8
Thus, we get, the correct option is,
A)The graph passes through the point (0, 3), and for each increase of 1 in the x-values, the y-values increase by 1.8
