PLEASE HELP wiTH ALL OF THEse. I DON'T KNOW WHERE TO START---THANKS!
1. At 2pm the number of bacteria in a colony was 100, by 4pm it was 4000. Write an exponential function to model the population y of bacteria x hours after 2pm.
2.Using the information in problem 1, how many bacteria were there at 7pm that day?
3.Radioactive iodine is used to determine the health of the thyroid gland. It decays according to the equation y = ae-0.0856t, where t is in days. Find the half-life of this substance.
4. An anthropologist finds there is so little remaining Carbon-14 in a prehistoric bone that instruments cannot measure it. This means that there is less than 0.5% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The question is:
y = c e^kx
find c and k
at x = 0, y = 100
so
100 = c (1)
so c = 100
at x = 2, y = 4000
so
4000 = 100 e^2k
ln 40 = 2 k
3.69 = 2 k
so
k = 1.84
so
y = 100 e^(1.84 x)
2) I think you can do that now
3)
At t = 0, y = a
what is t when y = a/2
a/2 = a e^-.0856 T
.5 = e^-.0856 T
ln .5 = -.0856 T
you take it from there
Look up the half life of C 14. You have it.
Then how many half lives is .5% = .005
(1/2)^n = .005
n ln .5 = ln .005
n * -.693 = -5.3
so we know that the thing is at least n years old
age >/= 7.65 half lives
I love you Damon!!!
name the sets of numbers to which -7 belongs.
1. To write an exponential function to model the population y of bacteria x hours after 2pm, we can start by looking at the given information.
At 2pm, the number of bacteria was 100, and by 4pm, it was 4000. This means that in 2 hours, the population increased by a factor of 4000/100 = 40.
Using this information, we can write the exponential function as: y = a * (40)^x, where a is the initial population at 2pm.
2. To find the number of bacteria at 7pm, we need to determine the number of hours from 2pm to 7pm.
Since there are 12 hours from 2pm to 4pm, and another 3 hours from 4pm to 7pm, the total number of hours is 12 + 3 = 15.
Using the exponential function from problem 1, y = a * (40)^x, we can substitute x = 15 into the equation to find the population at 7pm.
3. To find the half-life of the radioactive iodine, we need to determine the time at which the population decays to half its initial value.
In the equation y = ae^(-0.0856t), we know that y is the current population, and a is the initial population.
Setting y = a/2, we can solve for t to find the half-life.
4. To determine how long ago the person died, we need to use the decay of Carbon-14.
Since there is less than 0.5% of the Carbon-14 remaining, we can find the number of half-lives required for the population to decrease to such a low level.
Using the half-life of Carbon-14, we can multiply it by the number of half-lives to find the time elapsed.