Help solve step by step 1 You have 250mg of an unknown subst

Help solve step by step:

1. You have 250mg of an unknown substance and are told it has a half-life of 10years. You set up the following equation-- solve K.

y= Ce ^kt

a. -0.069

b. 0.068

c. - 0.693

d. 1.2

2. You have found k=0.1 when working out a certain half-life problem. How much of the substance will be left after 10 years if you start with 500mg?

a. 113 mg

b. 100 mg

c. 184 mg

d. 562 mg

3. Warfarin is a drug used as an anticoagulant. After administration of the drug is stopped, the quantity remaining in a patients body decreases at a rate proportional the quantity remaining. The half -life of warfin is 37 hours. How many hours does it take for the drug level in the body to to be reduced to 25% the original level?

a. 48

b. 74

c. 92

d. 106

Please provide step by step

Thank you

Solution

t(1/2) = 10

y = Ce^(kt)

125 = 250 * e^(k*10)

125/250 = e^(10k)

1/2 = e^(10k)

10k= ln(1/2)

k = 1/10 * ln(1/2)

k = -0.0693147180559945

Option A

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y = Ae^(-kt)

y = 500e^(-0.1*   10)

y = 183.9397205857211608

Option C

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t(1/2) = 37

So, k = -ln(2) / 37 = -0.0187337

y = Ae^(kt)

0.25A = Ae^(-0.0187337 * t)

0.25 = e^(-0.0187337t)

ln(0.25) = -0.0187337t

t = 74