How to a put this into an algebra equation?

Question

Week 1: 3 birds infected

Week 2: 15 birds infected

Week 3: 75 birds infected

Week 4: 375 birds infected

I. Name the two variables in this situation. Which is independent? Which is dependent?

Answer 1

Time and number of birds infected. I would say time is the independent, infected birds is the dependent:

Equation could be :

t= Time

No. of Birds infected, NBI= a*t+b

This is a linear equation, so we need only 2 data points to calculate the constants a and b. Since we have 4 data points, it may turn out that the best equation to fit the data is a higher order equation, such as a quadratic rather than a linear.

To get a and b

Lets take

P1:  t=1 (week),  NBI=3

P4:  t=4 (weeks), NBI=375

1)     3 = 1a+b

2) 375 = 4a+b

a=3-b, then 375=4(3-b)+b or 363=-3b or b=-121, then a=3-(-121)=124

So, here is a linear equation NBI = 124t-121

Now use the equation to see how well it predicts data points 2 and 3

P2(2,15)

NBI = 124t-121 =124(2)-121=127 instead of 15 not too good

P3(3,75)

NBI = 124(3)-121=251, not good either

This tells you that the linear equation is not a good fit to the data, and is not the right answer.

Of course, only having 4 data points you can play with the equation that fits, which obviously is

NBI= 3*5^(t-1),

however, if one has thousands of data points, like in medical research, to select a model that best fits the data collected.  The fact, that the 4 data points exactly fit one curve, suggests that the question was contrived, and you better focus on learning something about Numerical Analysis.

Answer 2

t = time in weeks, where t >= 1 and t is an element of the Integer set. t is an independent variable.

b = the number of birds infected. b is a dependent variable dependent on t

b = 3*5^(t -1)

Answer 3

Y=3*5^x,

so x is independent and y is dependent

Answer 4

i would say y = 3* 5 ^ (x-1).

lets try to see if i am right:

week 1 means x = 1 => y = 3* 5 ^ 1-1 = 3* 5^0 = 3*1= 3

week 2 => y = 3*5 = 15

week 3 => y = 3*5^2 = 3*25 = 75.

week 4 => y = 3* 5 ^3 = 3*125 = 375.