x (days) 0 20 40 80 120 160 W (worms) 50 48 45 36 20 3 Biology Some types of wor
ID: 3103053 • Letter: X
Question
x (days) 0 20 40 80 120 160
W (worms) 50 48 45 36 20 3
Biology Some types of worms have a remarkable ability
to live without moisture. The following table from one
study shows the number of worms W surviving after x
days without moisture.
(a) Use the equation W = -0.0014x^2 – 0.076x + 50 to find W for each x-value in the table.
(b) Discuss how well this equation approximates the
data.
(c) Use this equation to estimate the number of worms on
day 60 and on day 180. Which answer is most accurate?
Explain.
Explanation / Answer
First, take the time to understand what x(days) and W (worms) means in the equation. The question helps you a lot by already assigning a variable to each (x and W respectively)
(a) This part should be fairly intuitive. You are given the equation:
W = -0.0014x^2 – 0.076x + 50
It asks to find each W for the given values of x. Since you are looking for W, you plug in the x values. For example you first plug in x=0 days. This gives, W=50. (Check, does this make sense with the table of information? Yes it does! great!)
next, plug in x=20 days ---> W = -0.0014(20)^2 – 0.076(20) + 50 = 47.92 (check, does this make sense with the table of info? they show W to be 48 when x is 20, so yes! )
Keep doing this for every x value. You can finish the rest on your own now that you understand.
(b) Now that you have your answers to part (a), compare them to the W values in the given table. How close are they? You'll noticed with the first two we worked out together, at x=0, there was no error in the formula! We calculated the same answer as in the table. Then with x=20, we calculated W=47.92, which was still very close! only 0.08 error.
Notice, the answers you got for part (a) have a little bit more error each time. (You'll need this bit of information for the next part!)
(c) Now that you've done part (a), this part should seem easier to you. Think about what they are asking for...an estimate for the number of worms (w). What is given? Right, days. So just like in part (a), plug in the number of days into the equation.
First, you'll plug in day 60
W = -0.0014(60)^2 – 0.076(60) + 50 = 40.4
You can solve for 180 days. What answer did you get? (mine was negative) Doesn't seem to make sense does it? Don't worry, it shouldn't! Not long after 160 days, all the worms should be dead and the approximation should go to zero, but the equation doesn't account for that.
Now, think you can answer the last question to part (c)? Which approximation is more accurate, for 60 days or 180 days? (I'll give you a hint: it sure doesn't make sense to have a negative amount of worms!!)
I hope this helped!
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