Answer:
Option C is correct.
The kind of growth model is shown in the table is exponential
Step-by-step explanation:
Exponential growth function is in the form of : [tex]y = ab^x[/tex] ......[1]; where a is the initial value and b> 0.
Consider any two point from the table:
(1 , 5) and ( 2 , 25)
Substitute these in the equation [1] we get;
[tex]5 = ab^1[/tex] ......[2]
[tex]25 = ab^2[/tex] ......[3]
Divide equation [3] by [2] we have;
[tex]\frac{25}{5} = \frac{ab^2}{ab}[/tex]
Simplify:
[tex]5 = b[/tex]
Now substitute this value in equation [2] we get;
[tex]5 = a \times 5[/tex]
Divide both sides by 5 we get;
[tex]\frac{5}{5} = \frac{5a}{5}[/tex]
Simplify:
1=a or a = 1
Therefore, the table shown the exponential growth function is, [tex]y = 5^x[/tex]
