Farmer Jones has 140 feet of fencing to construct a rectangular corral.
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Okay, the exponential function is
The start price of it in t=0 is 3,500, as we can see on the graph. Then, the function becomes
Let's see at t=2, where the price is g=2000:
Take natural logarithm:
So, the difference between t=0 and t=2 is
And then we get the change of x in one year equal to 0.035.
So, the final equation is
You can insert any t and see that it is correct, for example t=7
The start price of it in t=0 is 3,500, as we can see on the graph. Then, the function becomes
Let's see at t=2, where the price is g=2000:
Take natural logarithm:
So, the difference between t=0 and t=2 is
And then we get the change of x in one year equal to 0.035.
So, the final equation is
You can insert any t and see that it is correct, for example t=7
In order to find any of the info we need we have to find the first derivative of the equation. If 
, then 
. We are told to find the slope at point (1, 7). Using that x value in our derivative will give us the slope of the line at that point. y' = -(1)^2+8. So y' = 7. That's the slope of the line. Now we will use that slope along with the x and y coordinate in the slope-intercept form of a line to solve for b. 7 = 7(1) + b so b = 0. Our equation then is y = 7x. If you graph these in the same window on your calculator, you can see how perfectly that align at the given point. It's really quite perfect.