Here we have seven to the I power where I starts with one, and it ends with seven to the fourth power. Because you have to multiply every term by seven to get the next value, so we can actually write asset meditation.
#Psequel m1 series
And we can actually create a some, um, notation just by seeing really recognizing that this is a geometric series because every term is seven times the preceding one. So this is the end of their poems who were given the number of wife sacks, cats and kids. So this is the number of kittens, and we're also given information that every kitten, uh, are saying that this is the end. So wives, number of wise and number of Saks, and this is the number of cats and every cut seven kids, So seven cute times seven another seven. So this is a number of kings writers, actually. And every Zack every cut has seven kittens. Square is seven squared just seven times seven and re multiplied by the other seven here. So seven times seven and each of the seven sacks each of the sacks have seven cats. So seven wise has each of them have seven sacks. And the poem, briefly summarized, consists of, um, the narrator bumping into a man with seven wives to seven wives, a man with seven waas and every more writing this as a some and every wife has seven sex. In this scenario, we have were given a poem that refers to a quaint old village in England's and were asked to create a sequence or expressed the sum of a sequence of the total amount of objects at the narrator of the poem Encounters. Um considering that Pluto is distance and it's uh revolution period is exactly modeled by this data.
So we'll see that this linear model perfectly fits this data pretty much. Um for its value, which is exactly what is given to us in the problem. And so we'll have this cancellation giving us P is equal to eat to this power, which gives us simply approximately 240 8.5. It's equal to approximately 5.5 15 Now we can just raise both sides with the power. And we'll see that this corresponds to 1.5 Natural Log during entry five. So what we can do is to find Peewee do first natural log of P sequel to 20.5 years euro times. So if we want to go ahead and find the Pluto, which is Pluto, if D is equal to 39.5, we get to plug in the natural log of D.
#Psequel m1 plus
So what we have to remember is that this is actually something this this this line is if we go ahead and write the units and it actually represented Natural log of P is equal to 1.5, types of natural log of B plus your points. So the next thing we want to do is use this linear model to predict uh The period of Pluto if its distance is 39.5. And if you go ahead and plot it, we end up with this, you can see it above. So we can write this model as why is equal to, says approximately 1.500 X. is equal to 1.499 and B is equal to 0.001. So we end up with why? Because the experts be Where a. So we can go ahead and run um linear regression on the calculator. So it it appears to be this this straight line. And this is what the transformation were plotting the following Ellen T. So this data appears to be a Schrade through like that.
So we have this picture here and we'll notice that it looks very linear. So we want to make a scatter diagram for all of these points um using our graphing calculator and I went ahead and do that already. So these distance have been normalized so that Earth is exactly one unit away from the sun, and that period is one unit. Okay, so we have this table containing uh the planet's average distances D from the sun and then p the period of revolution.
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