5 a Six malters of a drug are injected into the emains in the MAT 0318 Saring 20

Question

5 a Six malters of a drug are injected into the emains in the MAT 0318 Saring 2018 Saughter 75% of the original amount remains "the hou. et a dug are injected into the bisenew mount present remains in the bloodstream. Complete made a mistake. ne tabie below. If you do not get 2.53 mt (rounded) for 3 days later, you have CALCULATION Hour Late Hour Lat 3 Hour Later h Hour Later Non-text b. What is the equation that relates the amount of the drug in the bloodstream to the number of hours? t What percent of the drug is lost from the bloodstream during each hour? c. (modified) Use the equation to caloulate the number of militers in the blood stream aer 10 hours? Assuming that interest is compounded monthly, the account at some time in the future. Show your work!! formula below computes how much money will be in your F Pl1 where: F is Future Value P is the amount invested or principal i is the interest per compounding period n is the number of compounding periods Find the Future Value of a S3… deposit if the annual rate is 7.S% compounded monthly for 10 years (hint the correct answer is somewhere between $6200 and $6500). Express you answer in a b. Determine how much money must be invested today at an annual rate of 6% compounded monthly if the sum of $15,000 is desired 15 years from now (hint the correct answer is somewhere between $6000 and $6200)Express you onswer in a sentence which relates your numerical answer back to

Explanation / Answer

1)

a) (100% - 75%) ,i.e., 25% of the drug is lost from the bloodstream during each hour.

b) The equation that relates the amount of the drug in the bloodstream to the number of hours is

A = 6*(75/100)T

where A = remaining amount of the drug, T = number of hours.

c) Putting T = 10 in the above equation we get,

A = 6*(75/100)10 = 0.34 millilitre

Hence, after 10 hours, there is 0.34 millilitre of the drug in the bloodstream.

2)(a) Let, P be the amount invested and i be the interest which is compounded monthly.

Then, after 1st month, the amount will be = P + P*i = P(1+i).

Again, after 2nd month, the amount will be = P(1+i) + P(1+i)*i = P(1+i+i+i2) = P(i2+2i+1) = P(1+i)2

After 3rd month, the amount will be = P(1+i)2 + P(1+i)2*i = P(1+i)2*(1+i) = P(1+i)3

Proceeding in this way we get,

After nth month, the amount will be = P(1+i)n.

Therefore, F = P(1+i)n.....(i) where F = future value.

(b) Here given, P = $3000

and, i = (7.5%)/12 = 7.5/1200 = 0.00625   [Since 7.5% is the annual rate]

and, n = 10 years = 120 months

Putting this values in (i) we get, F = $[3000*(1+0.00625)120] = $[3000*1.00625120] = $6336.19

Hence, the future value is $6336.19

(c) Here given, F = $15000

and, i = (6%)/12 = 6/1200 = 0.005 [Since 6% is the annual rate]

and, n = 15 years = 180 months

Putting this values in (i) we get,

P = $[15000/(1+0.005)180] = $[15000/1.005180] = $6112.24

Hence, $6112.24 must be invested today.

Hours Calculation Milliliters Initial 6*(75/100)0 6 1 hour later 6*(75/100)1 4.5 2 hours later 6*(75/100)2 3.38 3 hours later 6*(75/100)3 2.53 4 hours later 6*(75/100)4 1.90 h hours later 6*(75/100)h 6*(75/100)h

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