20 points What is the linear function equation represented by the graph?
1 answer:
You might be interested in
Answer:
Yes, but it is not linear. It is exponential :
Step-by-step explanation:
On the first day we have 5 bacteria.
On the second day we will have 5*2 = 10 bacteria.
On the third day we will have 10*2 = 5*2*2 = 5*2^2 = 20 bacteria.
On the fourth day we will have 20*2 = 5*2*2*2 = 5*2^3 = 40 bacteria.
We can see that
,
where x is a number of days and f(x) gives us the number of bacteria.
(a) Suppose 
is a solution for this recurrence, with 
. Then
So we expect a general solution of the form
With
, we get four equations in four unknowns:
So the particular solution to the recurrence is
(b) Let
be the generating function for 
. Multiply both sides of the recurrence by 
and sum over all 
.
From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of, ideally matching the solution found in part (a).
So we expect a general solution of the form
With
So the particular solution to the recurrence is
(b) Let
From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of