When asked to find P(1), P(2),...P(5) for the difference equation P(n+1)=(1 +r) P(n), with r= .1 and P(0)= $1000. Are we to just plug in the numbers to the equation and solve or am I missing a step?
You are using r = .1 and P(0) = $1000. This works just like any other recurrence relation:
Substituting n = 0 you get
P(0 + 1) = (1 + .1) P(0) or
P(1) = 1.1 * $1000 = $1100.
Substituting n = 1 you get
P(1 + 1) = (1 + .1) P(1) or
P(2) = 1.1 * $1100 = $1210.
Then you substitute n = 2, 3 and 4 in order to get P(3), P(4) and P(5).
When asked to suppose that y=f(x)=5(1.276^x). Find the coordinates of the basic points (0,f(0))and (1, f(1). The points are separated by a horizontal distance of 1 unit. What is the ratio between the y values. Are you asking for the slope between these two points of for the value of each point?
f(1) = 5 ( 1.276^1) = 6.38 (I think). If that's right then the point (1, f(1) ) is (1, 6.38).
f(0) = 5 (check that out) so (0, f(0)) = (0, 5).
The ratio of the y values is
ratio = second y value / first y value.
What are the y values of the two points, and what is their ratio?
When asked to find the basic points of an exponential function is this always going to be, for instance, (0,1)and (1,1) or does that depend on the numbers that are already in the problem?
The basic points will be the t = 0 and t = 1 points, and the y values will indeed depend on the specific function.