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The number of bees_ P in a colony doubles every 3 years Ift is measured in years and Po is the initial number of bees, then-3 P = Po20 P = Po2st0 P = Po2tP = Po32P ...

Question

The number of bees_ P in a colony doubles every 3 years Ift is measured in years and Po is the initial number of bees, then-3 P = Po20 P = Po2st0 P = Po2tP = Po32P = Po3

The number of bees_ P in a colony doubles every 3 years Ift is measured in years and Po is the initial number of bees, then- 3 P = Po2 0 P = Po2st 0 P = Po2t P = Po32 P = Po3



Answers

Critical Thinking In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice? Check each of the requirements of a binomial experiment and give the values of $n, r$, and $p$.

Here, we wanna find the formula for Petey and P. It's a function, but it's unbearable key here and to find the exact formula. When you do know the while you off this sea and cape to self to unknown variables, we need two questions to do that and the notice that we have two conditions. The first dates at the doubling time in seven years ends in P zero equals to 100. So burial, constructive first equation and the second question separate. Be so consider the 1st 1 So recall that the Dublin time as a tree long to over Kate but ever goes through this myself here again. So suppose I were double in time as upper level upper case logic T. And, uh, we won't see each of the power off k t plus our pro kissed E because to to see each of the power off K model Christy and then here is just we can cancel seeing the both side. Here's just a J d. Power of K Lord kissed t and e to the part of K I protest e because to to lead to the power off K Laurel Castillo and then we can cancel both term here. So we often Katie, Because too long, too. And then we can know the Dublin time. It's actually long two over. So we know here suffering time in seven years. That means long to over Kay as seven years. Therefore, we can mountain k equals too long to overstep. And then we need the second you creations. We know the value off p and zero should be 100. That means C E K. What client zero should be 100. This is actually just Cyril. So we have e see each of the power of Cyril and 100. And then since e ticket power off, Cyril is just one the captain, see, because to 100. Therefore, we already obtained the well off the two variables. So we can know as just equals to 100. Multiply you to the power off long to hover. Simon T therefore, can often the answer. But if you want the formula to look master, we can actually put here to be 100 multiplied into the power off lawn too. And the multiply each of the power e over seven and hear this by definition, is just too. So this formula should be 100 and multiply two to the power off T over seven. You can take which ever formula you lack here.

This question asks for values for the parameters and the initial quantity and percent rate. What we knows that we can take p of 08 of the fourth, which is 18. Divide by P of Oh, a cube, which is 20 to get an A of 0.9. Now plug me into the equation. Pivo is 20 over a cube. We end up with p of oh, is 27 points for three. These are two values which we're gonna need for part B. Now Part B asks us, giving these two values we no need to figure out the percent rate of change. We can do this using the formula A minus one if a 0.90 point nine minus one is negative 0.1, also known as negative 10%.

So this problem gives us a quantity p changing best on the change in terrible T. So look has the first problem. We're asking what at one time t as people, certain soapy, only depend on the water off t. Then we can just hopped in a equations with that. So you wanted tea so that PT equal Sutin, We can just put the question here than you to the power off five t equals two tin And then the best way for us to try to solve a question you involving the exponential as to take long at both sides. Then we have a long beat in power off five t because to 10 notice that was so good talk concert in the right hand side. But for the left hand side were a large too simply father's expression to be 50. But the definition off X one, the shop ee Then we got just five t equals two long turn ends in t just equals two long turn over fight So here in the first part off this problem is so then we can look at the second problem party here we are asking what is a doubling time for P. So we can. That's the doubling time to be the uppercase T and Ali Business line moot. Okay, then we won't know at one time this are for kids. T would p t last t would you cause too, two times p. Laura has t That's just followed by the detonation off the stubborn in time. And then we can put such expression into a question again. So they have each of the power off by lower case t plus Separatist E because to two times need to be cut off by lower Christine. And the mega separates this expression to be you to the power off farty multiply e to the father off five uppercase t because through to aging, power off slack t. So for here, what happened to value its that lower case T as we can always cancel this to turn, don't we often e to the power off five applicants t equals to two. And remember, result here I remember one less off the exponential off the we can try to take long at the both side of the equation. So we get along each the power off five Africa's tea because too long too. And so is he here has just five. I put his tea. He calls too long to which yells t eco's too long to over five and this upper kissed He is doubling time we want here. Is it? Actually this is a result were memorizing cause will be used a lot for Petey You call to me Kai t The doubling time floors is is just long to over. Okay, This is a really important result in the tech boot textbooks so that maybe we can all remember it.

Okay, were asked how many wolves will have? Well, the habitat have after the use that sits P of three is you go to 558 which took this into our formula. And then if you plug this into the cancel it and you get approximately 37 wolves.


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