1) The normal healing of a wound can be modeled by the exponential function- Age

Question

1) The normal healing of a wound can be modeled by the exponential function- Age sn, where Ao represents the initial area of the wound and A represents the area of the wound a wound had an initial area of 100 cm after n days. Suppose a. How large should the area of the wound be after 3 days? b. How large should it be after 10 days? c. How many days will it take to reach an area of 70 cm2 d. How many days until the area is 10 cm2? (2) A single pane of glass obliterates 10% of the light passing through it. The percent of light passing through n panes of glass is modeled by the function 100e-0.1n a. b. c. d. What percent of the light is blocked by 4 panes of glass? What percent of the light is blocked by 7 panes of glass? How many panes of glass are needed to successfully block 50% of light? How many panes will block 90% of the light? /n 3) The half-life of radium is 1690 years. Half-life is modeled by the function A-Awhere A represents the amount remaining after n years, Ao is the initial amount, t is the number of years that have passed, and n is the half-life. Suppose we started with 10 grams of radium. a. How much will be present after 50 years? b. How much radium will remain after 500 years? c. How much will remain after 5000 years? d. How many years until 4 grams remain? e. How many years until 2 grams are left? f. How many years until half a gram is all that remains of the radium? )Environmentalists are capturing bald eagles and moving them to a protected environment in order to regenerate the population. Past experience with this method has produced the function 500 1+8333e 0x62t to model the population after t years. a. What is the expected population in 10 years? b. What is the expected population in 20 years? c. When should the population reach 300? d. When should the population reach 1000? After the Chernobyl meltdown in 1986, hay in Australia was contaminated by iodine-131 9half-life years ). It is safe to feed the hay to animals once only 10% of the isotope remains in the hay. Use t /m , where P represents percent of contamination, t -years that have passed, and model alf-life. a. What percent remains after 10 years? b. What percent remains after 25 years? c. How long until the hay is safe to feed to the animals?

Explanation / Answer

3b) At = Ao (1/2)^t/n

radium after 500 years

At = 10 (1/2)^500/1690

At = 8.146

so, 8.146 remains after 500 years

e) 2 = 10 (1/2)^t/1690

2 / 10 = (1/2)^t/1690

ln (1/5) = t/1690 ln (1/2)

t = 3924.06 years

2 grams remains after 3924.06 years

3) 1/2 = 10 (1/2)^t/1690

1/20 = (1/2)^t/1690

ln (1/20) = t/1690 ln (1/2)

t = 7304.06

so, half a gram will remain after 7304.06 years

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