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kifflom [539]
3 years ago
11

BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!

Mathematics
2 answers:
mash [69]3 years ago
7 0
Part 1:

Given that a<span> store had 235 MP3 players in the month of January and that every month, 30% of the MP3 players were sold and 50 new MP3 players were stocked in the store.

</span>The number of MP3 players in the store after the previous months sale is given by 0.7f(n - 1) and <span>the number of MP3 players in the store after new MP3 were added is 0.7f(n - 1) + 50.

Therefore, the </span><span>recursive function that best represents the number of MP3 players in the store f(n) after n months is given by </span><span>f(n) = 0.7 x f(n − 1) + 50, f(0) = 235, n > 0



Part 2:

The average rate of change of a function from a to b is given by

average \ rate \ of \ change= \frac{f(b)-f(a)}{b-a}

Given that the </span><span>equation showing the value of her investment after x years is given by

f(x)=500(1.05)^x

Thus, </span><span>the average rate of change of the value of Sophia's investment from the second year to the fourth year is given by

Average \ rate \ of \ change= \frac{f(4)-f(2)}{4-2}  \\  \\ = \frac{500(1.05)^4-500(1.05)^2}{2} = \frac{607.75-551.25}{2}  \\  \\ = \frac{56.5}{2} =28.25

Therefore, the </span><span>average rate of change of the value of Sophia's investment from the second year to the fourth year is 28.25 dollars per year.</span>

tekilochka [14]3 years ago
5 0
<span>1. f(n) = 0.7 x f(n â’ 1) + 50, f(0) = 235, n >= 0 2. 28.25 dollars per year 1. For this problem, let's construct the recursive formula ourselves. We know that f(0) will be 235 since that's the original stock and that n has to be greater than or equal to 0 (n=0 represents the starting stock). So we have f(n) = ?, f(0) = 235, n >= 0 Now each month we sell 30%, so we're left with 70% of the previous month's stock (100% - 30% = 70%). So let's take that into account for our function. f(n) = 0.7 x f(n-1), f(0) = 235, n >= 0 And each month we get another 50 MP3 players. Let's add that into our function. f(n) = 0.7 x f(n-1) + 50, f(0) = 235, n >= 0 And that's our answer. 2. Since we've been given the function f(x) = 500(1.05)^x, let's calculate the amount of money that we have after 2 years and 4 years. f(2) = 500(1.05)^2 = 551.25 f(4) = 500(1.05)^4 = 607.75 Now get the difference in money between those years. 607.75 - 551.25 = 56.50 And since we're talking about a period of 2 years and we want the average rate per year, divide by 2. 56.50 / 2 = 28.25 So the average change from year 2 to year 4 is $28.25 per year.</span>
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