A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 3^x = 5x − 1.

Explain to the biologist how she can solve this on a graph using a system of equations.

Question

A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 3^x = 5x − 1.

Explain to the biologist how she can solve this on a graph using a system of equations.

anonymous · Answer

@tkhunny

tkhunny · Answer

Well, we are talking about real flies and real lizards, so we get to ignore everything negative. First Quadrant Only!

Graph y = 3^x and y = 5x - 1 on the same coordinate axes and see if anything jumps out.

anonymous · Answer

2,9?

anonymous · Answer

Oh! Then that would be the answer since that's where they intersect right?

tkhunny · Answer

That's the idea, but don't get fooled by fake solutions.

|dw:1448744991244:dw|

All the flies are eaten by the first intersection.  They can't regenerate and be eaten again at the second intersection.  Just jeep your eyes out for such foolishness.  Real problems should make real sense.

anonymous · Answer

So 2,9 isnt the real solution???

tkhunny · Answer

I don't know. Did you find two or just one.

anonymous · Answer

1

anonymous · Answer

A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 4% of 70%.

Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.

anonymous · Answer

Can you please help??

tkhunny · Answer

Normally, one question per post.  This is quite a leap from the last question.

So, 5% of the population scores less than 4% and another 5% of the population scores higher than 70%.  It the distribution symmetric?

anonymous · Answer

not really

anonymous · Answer

the confidence interval is probably 90%

tkhunny · Answer

Why isn't the distribution symmetric?
Where did you obtain your guess of 90%?
Notice that it says "seniors will".  We're not making a prediction for a single student.

anonymous · Answer

Thanks for your help<3