All the functions grow with x except B that decreases when x grows. That i your function. Also check that when you divide the population of two consecutive years, the ratio remains 0.79 approx
The solution is B
Answer:
Option B is correct.
Exponential model are the data best represented.
Equation: [tex]y = 98 \cdot (0.79)^x[/tex]
Step-by-step explanation:
An exponential function is in the form of [tex]y= ab^x[/tex] .....[1] where a is the initial value and b≠0 , b > 1.
Consider any two points from the table;
(0, 98) and ( 1, 77)
Then substitute these in [1];
For (0, 98)
x = 0 and y = 98 substitute in [1] we get;
[tex]98 =ab^0[/tex]
98 = a
Similarly, For (1, 77)
we have;
[tex]77 =ab^1[/tex]
77 = ab
Substitute the value of a =98 we get;
[tex]77 = 98b[/tex]
Divide both sides by 98 we get;
[tex]\frac{77}{98} = \frac{98b}{98}[/tex]
⇒ b = 0.79
We get an equation; [tex]y = 98 \cdot (0.79)^x[/tex]
Therefore, the data represent here is, Exponential function.
also, an equation to model the data is; [tex]y = 98 \cdot (0.79)^x[/tex]
