5. medicine taken by a patient breaks down in the patients blood stream and dissipates out of the patients…

5. medicine taken by a patient breaks down in the patients blood stream and dissipates out of the patients system. suppose a dose of 60 milligrams of anti - parasite medicine is given to a dog and the medicine breaks down such that 20% of the medicine becomes ineffective every hour. how much of the 60 milligram dose is still active in the dogs bloodstream after 4.25 hours?\n6. a manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. the function is c(x)=5,000 + 1.3x.\n a. what is the cost of 2,000 items?\n b. if costs must be kept below $10,000 this month, what is the greatest number of items she can manufacture?\n7. juan and patti decided to see who could read the most books in a month. they began to keep track after patti had already read 5 books that month. this graph shows the number of books patti read for the next 10 days. if juan has read no books before the fourth day of the month and he reads at the same rate as patti, how many books will he have read by day 25?\n8. daniels print shop purchased a new printer for $35,000. each year it depreciates at a rate of 5%. what will its approximate value be at the end of the fourth year?

5. medicine taken by a patient breaks down in the patients blood stream and dissipates out of the patients system. suppose a dose of 60 milligrams of anti - parasite medicine is given to a dog and the medicine breaks down such that 20% of the medicine becomes ineffective every hour. how much of the 60 milligram dose is still active in the dogs bloodstream after 4.25 hours?\n6. a manufacturer keeps track of her monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. the function is c(x)=5,000 + 1.3x.\n a. what is the cost of 2,000 items?\n b. if costs must be kept below $10,000 this month, what is the greatest number of items she can manufacture?\n7. juan and patti decided to see who could read the most books in a month. they began to keep track after patti had already read 5 books that month. this graph shows the number of books patti read for the next 10 days. if juan has read no books before the fourth day of the month and he reads at the same rate as patti, how many books will he have read by day 25?\n8. daniels print shop purchased a new printer for $35,000. each year it depreciates at a rate of 5%. what will its approximate value be at the end of the fourth year?

Answer

5.

Explanation:

Step1: Determine the decay - factor

Since 20% of the medicine becomes ineffective every hour, the amount of active medicine remaining after each hour is 1 - 0.2=0.8. The initial amount of medicine (a = 60) milligrams, and the time (t = 4.25) hours. The formula for exponential decay is (y=a\times b^{t}), where (b) is the decay - factor.

Step2: Calculate the remaining active medicine

Substitute (a = 60), (b = 0.8), and (t = 4.25) into the formula (y = 60\times(0.8)^{4.25}). First, calculate ((0.8)^{4.25}). Let (x = 4.25), then ((0.8)^{4.25}=0.8^{4}\times0.8^{0.25}). (0.8^{4}=0.4096), and (0.8^{0.25}=\sqrt[4]{0.8}\approx0.9457). So, ((0.8)^{4.25}\approx0.4096\times0.9457\approx0.387). Then (y = 60\times0.387 = 23.22) milligrams.

Answer:

23.22 milligrams

6.

a.

Explanation:

Step1: Substitute the value of (x) into the cost - function

The cost function is (C(x)=5000 + 1.3x). We need to find the cost when (x = 2000). Substitute (x = 2000) into the function: (C(2000)=5000+1.3\times2000).

Step2: Calculate the result

First, calculate (1.3\times2000 = 2600). Then (C(2000)=5000 + 2600=7600).

Answer:

(7600)

b.

Explanation:

Step1: Set up the inequality

We know that (C(x)<10000), and (C(x)=5000 + 1.3x). So, the inequality is (5000+1.3x<10000).

Step2: Solve the inequality for (x)

Subtract 5000 from both sides: (1.3x<10000 - 5000), which simplifies to (1.3x<5000). Then divide both sides by 1.3: (x<\frac{5000}{1.3}\approx3846.15). Since (x) represents the number of items, the greatest whole - number value of (x) is 3846.

Answer:

3846

7.

Explanation:

Step1: Find Patti's reading rate

Patti starts with 5 books and reads for 10 days. From the graph, at (x = 10), (y) (the number of books) is 20. So, in 10 days, she reads (20 - 5=15) books. Her rate (r=\frac{15}{10}=1.5) books per day.

Step2: Calculate the number of days Juan reads

Juan starts on the 4th day and reads until the 25th day, so he reads for (25 - 4=21) days.

Step3: Calculate the number of books Juan reads

Since his rate is the same as Patti's ((r = 1.5) books per day), the number of books he reads (n=1.5\times21 = 31.5). Since we are talking about whole books, we can say he reads 31 books (if we consider whole - book counts).

Answer:

31 books

8.

Explanation:

Step1: Identify the formula for depreciation

The formula for exponential depreciation is (A = P(1 - r)^{t}), where (P) is the initial value, (r) is the rate of depreciation, and (t) is the time in years. Here, (P = 35000), (r=0.05), and (t = 4).

Step2: Calculate the value of the printer after 4 years

Substitute the values into the formula: (A = 35000\times(1 - 0.05)^{4}=35000\times(0.95)^{4}). Calculate ((0.95)^{4}=0.95\times0.95\times0.95\times0.95 = 0.81450625). Then (A = 35000\times0.81450625\approx28507.72).

Answer:

(28507.72)