anyone can help me out?

Paper assignment: Do all the following problems in a neatly organized fashion on another sheet of paper. Show all algebraic steps -- where indicated, write a full proof. Due on Thurs. 3/10 Some sample answers will be posted on canvas. No late work accepted.

I. Logarithmic scales: (day 1)

1) The Richter scale is a logarithmic scale, with an increase of one on the scale corresponding to a ten-times increase in the intensity of the earthquake. For the problems that follow,

· earthquake A was rated 3.2.

· earthquake B was rated 5.2.

· earthquake C was rated 6.6.

a) What would the rating be for a quake that was 10 times as intense as A?

b) What would the rating be for a quake that was 100 times as intense as A?

c) What would the rating be for a quake that was 1/100 as intense as A?

d) What would the rating be for a quake that was 1/10 as intense as A?

e) What would the rating be for a quake that was 10,000 times as intense as A?

f) What would the rating be for a quake that was 10 times as intense as C?

g) What would the rating be for a quake that was 100 times as intense as C?

h) What would the rating be for a quake that was 1/100 as intense as C?

i) What would the rating be for a quake that was 700 times as intense as A?

j) What would the rating be for a quake that was 50 times as intense as C?

k) What would the rating be for a quake that was 25 times as intense as B?

l) What would the rating be for a quake that was 1250 times as intense as B?

m) What would the rating be for a quake that was 310 times as intense as C?

n) What would the rating be for a quake that was 700 times as intense as C?

o) Compare the intensities of A and B with a complete sentence.

p) Compare the intensities of A and C with a complete sentence.

q) Compare the intensities of B and C with a complete sentence.

r) Two quakes hit the same area one week apart. The first was rated 3.0, and the second was rated 7.0. Compare the intensities of the earthquakes with a complete sentence.

s) Two quakes hit the same area one week apart. The first was rated 4.0, and the second was rated 6.5. Compare the intensities of the earthquakes with a complete sentence.

t) Two quakes hit the same area one week apart. The first was rated 5.5, and the second was rated 7.0. Compare the intensities of the earthquakes with a complete sentence.

u) Two quakes hit the same area one week apart. The first was rated 8.1, and the second was rated 6.1. Compare the intensities of the earthquakes with a complete sentence.

II. Exponential growth and decay: (day 2) Round to 5 decimal places when necessary.

2) A population of wombats has 5000 animals when we start monitoring. After 1 year, there were 5375 wombats. Assume a consistent, exponential growth pattern

a) Write an equation with x = # of years, and f(x) = # of wombats.

b) What is the percent growth each year?

c) Find the population after 6 years.

d) Find the population 8 years ago.

e) Find the time it takes for the population to reach 9000 wombats; Show your algebraic steps in a two-column proof format. (with reasons for each step)

f) Write and simplify an equation with x = # of weeks, and g(x) = # of wombats.

g) Write an equation for x= # of years, and f(x) = number of wombats(same as A) but using base e.

3) A sample of Nachesium (Nm) loses its radioactivity in an exponential decay pattern. At time zero, we have a sample of 400 grams that is radioactive, and after one day, only 383 grams are left radiating.

a) Write an equation with x = # of days, and f(x) = # of grams radioactive (Nm) left.

b) What is the percent decrease each day?

c) Find the amount of (Nm) radioactive after 7.5 days.

d) Find the amount of (Nm) radioactive 6 days ago, assuming a consistent pattern of decay.

e) Find the time it takes for the sample to reach a safe level of 35 g grams radioactive (Nm) left; Show your algebraic steps in a two-column proof format. (with reasons for each step)

f) Write and simplify an equation with x = # of weeks, and g(x) = # of grams radioactive (Nm) left.

g) What is the percent decrease each week?

h) Write and simplify an equation with x = # of hours, and k(x) = # of grams radioactive (Nm) left.

i) Write an equation for x= # of days, and f(x) = number of grams radioactive (Nm) left (same as A) but using base e.

4) A sample of Kittitasium has a half-life of 30 days. We start with a sample of 1200 grams radioactive.

a) Write an equation with x = # of days, and f(x) = # of grams radioactive Kittitasium left, using a base of ½.

b) Simplify your equation from part a, rounding the base to 5 decimal places.

c) What is the percent decrease each day?

d) Write an equation for x= # of days, and f(x) = number of grams radioactive Kittitasium left (same as A) but using base e.

e) Find the amount of Kittitasium after 8.3 days.

f) Find the amount of Kittitasium 9 days ago, assuming a consistent pattern.

g) Find the time it takes for the sample to reach a safe level of 50 g grams radioactive Kittitasium left; Show your algebraic steps.

h) Write and simplify an equation with x = # of weeks, and g(x) = # of grams radioactive Kittitasium left.

i) What is the percent decrease each week?

j) Write and simplify an equation with x = # of hours, and k(x) = # of grams radioactive Kittitasium left.

5) A bacterial growth has 5700 organisms when we discover it (time = 0). After one day, there are 7100 organisms. Assume consistent exponential growth:

a) Write an equation with x = # of days, and f(x) = # of bacteria.

b) What is the percent growth per day?

c) Find the population after 7 days.

d) Find the population 10 days ago, assuming a consistent pattern.

e) Find the time it takes for the population to reach 13,000 bacteria; Show your algebraic steps.

f) Write and simplify an equation with x = # of weeks, and g(x) = # of bacteria.

g) What is the percent growth per week?

h) Write and simplify an equation with x = # of hours, and h(x) = # of bacteria.

i) What is the percent growth per hour?

j) Write an equation for x= # of days, and f(x) = number of bacteria (same as A) but using base e.

6) Iodine 131 is a radioactive material that decays according to the formula: ; is the initial amount, is the amount left after t days. Answer the following questions, given that we start with 1650 grams of Iodine 131.

a) Write an equation with x = # of days, and f(x) = # of grams radioactive Iodine 131 left, using a base of e

b) Rewrite your equation for part a without using e (i.e. use a decimal base). Round to 5 decimal places.

c) Find the amount of Iodine 131 after 17 days.

d) How much of the material was present 12 days ago, assuming a consistent pattern?

e) Find the time it takes for the sample to reach a safe level of 35 g grams radioactive Iodine 131 left; Show your algebraic steps.

f) Write and simplify an equation with x = # of hours, and g(x) = # of grams radioactive Iodine 131 left.

g) Write and simplify an equation with x = # of weeks, and L(x) = # of grams radioactive Iodine 131 left.