Question

can anyone solve a , b and c part

7 Chapter Task The Half-Life of Caffeine Caffeine is a stimulant found in many products, such as coffee, tea, pop, and chocolate. When you drink a cup of tea or eat a chocolate bar, you ingest caffeine. Your body breaks down caffeine slowly. As with other drugs, caffeine has a half-life in the body. The half-life of caffeine in a typical nonsmoking adult is 5.5 h. Caffeine Content (mg) 250 mL of Coffee Drip 165 Brewed 130 Instant 95 Decaffeinated 4 250 mL of Tea Brewed 45 Instant 35 Green tea 30 The caffeine content of many popular foods and drinks is listed in the table at the right. You can use the information from the table to write an equation to model the amount of caffeine in your system after drinking or eating foods that contain caffeine. Soft drinks (mean) 43 Chocolate bar 20 Energy drinks Espresso, double (2 oz) 70 80 A cup of brewed coffee has approximately 130 mg of caffecine in it Suppose you drink a cup of drip coffee at 9 a.m. How much caffeine is left in your body a i) 12:00 noon A. Task Checklist Did you show the calculations you used to determine the caffeine ) 8 p.m. i midnight? B. Suppose that in addition to your 9 a.m. cup of coffee at noon, you ate a chocolate bar and drank a cup of green tea. How can you calculate the additonal amount of caffeine in your system? Determine the total amount of caffeine in your body at noon. levels for part A? Did you remember to include the caffeine from the 9 am. cup of coffee in your calculations for part B? C. If you had nothing else to eat or drink that contained caffeine from Did you remember to write an equation that models this situation? noon onward, predict the amount of caffeine in your body at 8 p.m. Make a list of the food or drinks with caffeine you have had today Write the time you had each food or drink. Calculate the amount of caffeine that will be left in your body at 10 p.m. tonight. Use a table like the one below to record your data Did you include the table you created for part D? Caffeine Content Number of Hours until 10 p.m. Time Ingested Food or Drink (mg) Exponential Functions 447 NE

Answer 1

half life of caffine = 5.5 hr.

N(t) Noe

N₀ = intial concentration

t = time

In (2) t

= 0.126

In(2) λ. 5,5

A) Given We drank a cup of Drip coffee at 9 a.m.

i) caffine content at 12 noon.

time difference = 12 - 9 = 3 hrs

N(12 noon) = 165*e^-0.126*3 = 113.063 mg

ii) caffine content at 8 p.m.

t = 8 p.m. - 9 a.m = 11 hrs

N(8 p.m.) = 165*e^-0.126*11 = 41.262mg

iii) Caffine at midnight

t = 12 a.m. - 9 a.m = 15 hrs

N(12 a.m.) = 165*e^-0.126*15 = 24.927 mg

B) We have to apply law of conservation of mass in this problem.

Initially there will be caffine content at 12 noon because of the consumption of caffine at 9 a.m.

Now at 12 noon we ate a chocolate bar and a cup of green tea

hence the total concentration of caffine = 113.063 + 20+30 = 163.063 mg

C) Caffine in my body at 8 p.m.

initially for 9 a.m. consumption at 8 p.m. caffine content = 41.262 mg

again at 12noon weconsumed 50 mg of caffine (chocolate bar and a cup of green tea)

t = 8 hrs

N(8) = 50*e^-0.126*8 = 18.247 mg

now the total caffine content at 8 p.m. = 41.262 + 18.247 = 59.510 mg.