## number of asthma sufferers

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
santaclaus
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### number of asthma sufferers

The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let N represent the number of asthma sufferers (in millions) worldwite t years after 1990.

a. Write N as a linear function of t. What is the slope? Waht does it tell you about asthma sufferers?
I used 84 and 130 as x values and 1990 and 2001 for y values. I found slope to be 4 and 2/11 doing y-y1 over x-x1Then I found b and put the x, y values in -- but it doesn't look right:
2001=4 2/11 (130) + b? I found b to be -1457.6 What am I doing wrong? and I just said that as years go on, the number of asthma sufferers increase consistently?
.

b. Write N as an exponential function of t. What is the growth factor? What does it tell you about asthma sufferes?
for this I put f(t)=abt and then f(2001)=abt=130. then solved for b:
ab2001/ab1990=130/84. Then b11=130/84 and that equaled 0.018539371
so growth factor =b=1+r . Then, I tried to solve for a?
.

c. How many asthma sufferers are predicted worldwide in the year 2010 with the linear model? With the exponential model?
I am not sure how to answer this based on my answers above.

stapel_eliz
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The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let N represent the number of asthma sufferers (in millions) worldwite t years after 1990.
Since "t = 0" means "in 1990", then the two points they've given you are (t, N) = (0, 84) and (t, N) = (11, 130). So your slope value is fine, but should probably be left as an improper fraction: m = 46/11.

To find the line equation, try plugging the y-intercept, (t, N) = (0, 84), into the slope-intercept form, y = mx + b. (By changing the meaning of "t", you created a relationship which didn't "look right" in the context of the exercise.)
b. Write N as an exponential function of t. What is the growth factor? What does it tell you about asthma sufferes?
Try using the given definition of "t", as illustrated above, to get the required equation.

santaclaus
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### Re: number of asthma sufferers

so, to continue answering b)
does f(t)=f(0)ab0=84? because t =0? then do ab11/ab0=130/84? I still get the same answer as before, that b11=130/84 which then b=.0185309371, so a=84 because anything to the zero power is 1?

stapel_eliz
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so, to continue answering b)
does f(t)=f(0)ab0=84? because t =0?
I'm not sure where you're getting that the formula is "f(t) = f(t)abt"...?

Given f(t) = abt, we get f(0) = ab0 = a = 84 for t = 0.

For t = 11, we then get f(11) = (84)(b11) = 130. Solve this for the value of b, but use the exact value, being the radical form, not a decimal approximation!