A_n= a₁+(n-1)d
a₁ first term
n terms
d distance between each value
a_n= 12+(405-1)(5)=2032
If she can drive 4180 miles in <em>two </em>weeks, it would make sense that she would drive an average of <em>half </em>that distance in <em>one </em>week. Half of 4180 is 2090, so she averaged 2090 miles each week.
A vertical translation 1 unit down since for example x is 1, if u plug it in both equations it is f(1)=1*2-1 which equals f(1)=1 and the point is (1,1) for the other one, g(1)=(1-1)2-1 it equals g(1)=-1
The range of the equation is 
Explanation:
The given equation is 
We need to determine the range of the equation.
<u>Range:</u>
The range of the function is the set of all dependent y - values for which the function is well defined.
Let us simplify the equation.
Thus, we have;

This can be written as 
Now, we shall determine the range.
Let us interchange the variables x and y.
Thus, we have;

Solving for y, we get;

Applying the log rule, if f(x) = g(x) then
, then, we get;

Simplifying, we get;

Dividing both sides by
, we have;

Subtracting 7 from both sides of the equation, we have;

Dividing both sides by 2, we get;

Let us find the positive values for logs.
Thus, we have,;


The function domain is 
By combining the intervals, the range becomes 
Hence, the range of the equation is 
P=$24038.60 has to be invested to have $45000 after 19 years