I. Logarithmic scales:
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.
What would the rating be for a quake that was 10 times as intense as A?
What would the rating be for a quake that was 100 times as intense as A?
What would the rating be for a quake that was 1/100 as intense as A?
What would the rating be for a quake that was 1/10 as intense as A?
What would the rating be for a quake that was 10,000 times as intense as A?
What would the rating be for a quake that was 10 times as intense as C?
What would the rating be for a quake that was 100 times as intense as C?
What would the rating be for a quake that was 1/100 as intense as C?
What would the rating be for a quake that was 700 times as intense as A?
What would the rating be for a quake that was 50 times as intense as C?
What would the rating be for a quake that was 25 times as intense as B?
What would the rating be for a quake that was 1250 times as intense as B?
What would the rating be for a quake that was 310 times as intense as C?
What would the rating be for a quake that was 700 times as intense as C?
Compare the intensities of A and B with a complete sentence.
Compare the intensities of A and C with a complete sentence.
Compare the intensities of B and C with a complete sentence.
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.
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.
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.
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:
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
Write an equation with x = # of years, and f(x) = # of wombats.
What is the percent growth each year?
Find the population after 6 years.
Find the population 8 years ago.
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)
Write and simplify an equation with x = # of weeks, and g(x) = # of wombats.
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.
Write an equation with x = # of days, and f(x) = # of grams radioactive (Nm) left.
What is the percent decrease each day?
Find the amount of (Nm)radioactive after 7.5 days.
Find the amount of (Nm) radioactive 6 days ago, assuming a consistent pattern of decay.
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)
Write and simplify an equation with x = # of weeks, and g(x) = # of grams radioactive (Nm) left.
What is the percent decrease each week?
Write and simplify an equation with x = # of hours, and k(x) = # of grams radioactive (Nm) left.
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.
Write an equation with x = # of days, and f(x) = # of grams radioactive Kittitasium left, using a base of ½.
Simplify your equation from part a, rounding the base to 5 decimal places.
What is the percent decrease each day?
Write an equation for x= # of days, and f(x) = number of grams radioactive Kittitasium left (same as A) but using base e.
Find the amount of Kittitasium after 8.3days.
Find the amount of Kittitasium9 days ago, assuming a consistent pattern.
Find the time it takes for the sample to reach a safe level of 50 g grams radioactive Kittitasium left; Show your algebraic steps.
Write and simplify an equation with x = # of weeks, and g(x) = # of grams radioactive Kittitasium left.
What is the percent decrease each week?
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:
Write an equation with x = # of days, and f(x) = # of bacteria.
What is the percent growth per day?
Find the population after 7 days.
Find the population 10 days ago, assuming a consistent pattern.
Find the time it takes for the population to reach 13,000 bacteria; Show your algebraic steps.
Write and simplify an equation with x = # of weeks, and g(x) = # of bacteria.
What is the percent growth per week?
Write and simplify an equation with x = # of hours, and h(x) = # of bacteria.
What is the percent growth per hour?
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: A(t)=A0e-0.087t; A_0 is the initial amount, A(t)is the amount left after t days. Answer the following questions, given that we start with 1650 grams of Iodine 131.
Write an equation with x = # of days, and f(x) = # of grams radioactive Iodine 131 left, using a base of e
Rewrite your equation for part a without using e (i.e. use a decimal base). Round to 5 decimal places.
Find the amount of Iodine 131 after 17 days.
How much of the material was present 12 days ago, assuming a consistent pattern?
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.
Write and simplify an equation with x = # of hours, and g(x) = # of grams radioactive Iodine 131 left.
Write and simplify an equation with x = # of weeks, and L(x) = # of grams radioactive Iodine 131 left.