I am having a difficult time with this question. Any help whatsoever will be really helpful as I have been pulling an all nighter for my test at 4pm.
The question reads as follows:
Suppose that y=[2-log(100-x)]/0.29 can be used to calculate the number of years y for x percent of a population of 928 web-footed sparrows to die. Approximate the percentage (to the nearest whole percent) of web-footed sparrows that died after 5 years.
The answer is supposed to be 96% but I am just not getting it. I have a feeling its not hard but I'm missing something crucial.
Thanks for all the help!
.29*5=2-log(100-x)
log(100-x)=.55
100-x=3.55
x=96.4
=/
I still do not understand. This is my setup.
5=[2-log(100-x)]/.29
1.45 = 2-log(100-x)
-.55 = -log(100-x)
.55= log(100-x)
Now I am frozen there... If i take the log of both sides I do have 100-x on the right but obtain -.2596 for the left. The problem would equal 100.2596 and not 96.4.
In your setup, I am confused as to where the 100-x=3.55 came from.
Thank you so much, you don't understand how helpful you guys are for taking the time to help us.
1.45=2-log(100-x)
-.55=-log(100-x)
.55=log(100-x)
take the antilog of each side
3.458133892=100-x
You are taking the LOG of both sides. You want the antilog.
Thank you so much!!! I got it!
To approximate the percentage of web-footed sparrows that died after 5 years using the given equation, y=[2-log(100-x)]/0.29, you need to substitute x=5 and solve for y.
Here's the step-by-step process:
Step 1: Plug in x=5 in the equation:
y=[2-log(100-5)]/0.29
Step 2: Simplify the expression inside the logarithm:
y=[2-log(95)]/0.29
Step 3: Use the property of logarithms to rewrite the expression:
y=[2-log(5*19)]/0.29
Step 4: Use the property of logarithms to split the expression:
y=[2-log(5)-log(19)]/0.29
Step 5: Use a calculator to evaluate the logarithms:
y=[2-0.69897-1.27875]/0.29
Step 6: Simplify further:
y=[0.02228]/0.29
Step 7: Calculate the value of y:
y ≈ 0.0768
Step 8: Convert y to a percentage:
y ≈ 0.0768 * 100 ≈ 7.68%
Therefore, the estimated percentage of web-footed sparrows that died after 5 years is approximately 7.68%. The answer of 96% you mentioned seems to be incorrect. Double-check your calculations and make sure you followed the steps correctly.