# maths exponential functions

Hi I have a Maths quiz on Monday and i have been of sick for the past week. I received these review questions from my teacher via email and he isn't replying to my questions i really do not get these questions if someone can do these and explain to me how they did them it would be a massive help. There are a total of 21 questions to do but if i understand how to do these first few then im sure i will be able to do the test. thank you in advance if you can help.

1. Nuclear energy derived from radioactive isotopes can be used to supply power to space vehicles. Suppose the output of the radioactive power supply for a certain satellite is given by the function: p = 30 x 20.3t where p is the power output measured in watts and t is time in days.
a) What is the output of the power supply after 31 days?
b) How many days does it take for the power supply to double?

3. The amount of particulate matter left in solution during a filtering process is given by the equation p = 400 x 2-0.6x where p is the amount of particulate matter in grams and x is the number of filtering steps?
a) How much particulate matter us there before any filtering steps have been applied?
b) Find the amount of particulate matter after 5 filtering steps and
c) What would be the minimum number of filtering steps required to ensure that at least 75 percent of the matter was removed?

4. A teachers salary is determined by the equation s = 35 500 x 1.06t where s is the salary in dollars and t is the number of years of experience with the employee.
a) What is the initial salary of the employee?
b) By what percentage does the salary increase each year?
c) Find the salary of the employee once they have had 12 years of experience.
d) Draw a sketch of the employee’s salary over a typical career length. Your sketch should show the correct shape of the graph, have axis labels with units and have an appropriate scale.
e) Discuss how well you think the equation models a typical teacher’s salary with time.

5. The amount of carbon 14 in a living human is about 0.1 microcuries. The amount remaining in a human body after t years after death can be estimated by a = 0.1 (1/2) t/5730.
a) Is this a case of exponential growth or decay? How can you tell?
b) How much carbon 14 is remaining in a body after 2000 years after death?
c) This method was used to date the age of artifacts. For example, the amount of carbon 14 in king tut's body tosat is 0.06 microcuries. Based on this info, how long ago was king tut ruling Egypt?

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1. when you want to use an exponent, the ^ sign is most useful.

s=355000*(1.06)^(t) (problem 4)

s(deltat1)=35500*(1.06^((t+1))

s(deltat1)35500( 1.06^t * 1.06^1)

how much did it change?

ok, to help typing let
a=35500*1.06^t

percent change= [a(1+1.06^1)-a(1)]/a

= 1.06^1 which is not much, for percent multipy it by 100.

Now, 5.

any fraction taken to a positive power gets smaller, a decay.
a=.1(.5)^2000/5730
This is strictly calculator work.

Use your yx key, or if you want to use the ln key, then

lna= ln(.1)+ 2000/5730 * ln (.5)

then when you get ln a, a = e^lna

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bobpursley

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