Answer:
a) N = 1.9t + 191 millions
b) N = 191 × (1.00952852)ˣ
Step-by-step explanation:
a)
For a linear function; we use the expression:
y = mx + c
where;
m = slope (i.e when two points of model are given (x₁,y₁) and (x₂,y₂);
Thus;
c = intercept of y or the value of y when x = 0
So , let assume that we take year since 2000 as t .so that t=0 means 2000 ,t=5 means 2005 and t=10 means 2010 etc
now number of licensed driver is N and related to t linearly
Thus;
N = mt + c (1)
GIVEN THAT:
At 2000 ,when t=0 number of licensed driver is 191 million ,so N intercept (N value when x=0) is 191
The number of values of drivers is 191 million in 2000 (t=0)
and 210 million in in 2010(t=10). So to points in the model is (0,191) and (10,210)
However; the slope m can now be illustrated as :
Slope
m = 1.9
Now substituting the value of c and m to the above linear model ; we have:
N = 1.9t + 191 millions
b)
An exponential model have standard equation
here :
a is the value of y when x=0 and b is the base of exponential function
when a value of y other than for x=0 is known we can calculate b by just substituting and solving
we have N as exponential function of year t
Therefore;
Thus; if we take year since 2000 as t so that t=0 means 2000, t=10 means 2010 ....etc
At t=0 we have N=191 so a=191
so our exponential function is :
we know that at t=10 at 2010 ,N is 210;
then replacing all value and solving for b ; we have
Making b the subject of the formula by rearrangement ; we have :
Taking log of both sides;
we know log =b log a
Taking exponential with base 10 on both side
b = 1.00952852
Hence; our exponential model is :
N = 191 × (1.00952852)ˣ