1) Find how many times more intense is the earthquake which measures 7.5 on Richter scale than one which measures 6.7? (Richter scale states magnitude of the earthquake with a equation M = log I/S, where I is intensity of earthquake being measured, and S is intensity of the standard earthquake.)
2) The nth term of the geometric sequence is provided by = 27(0.1)^n-1 . Write first 5 terms and determine 10th partial sum.
3) Basketball is dropped from the original height of 9 feet and on every bounce, bounces up 2/3 the distance it fell. Determine how far will it have traveled by time it hits ground 4th time?
4) The lake is stocked with 1,500 young trout. If number of original trout alive after x years is provided by function P(x) = 1,500 e^-0.4x, find when will there be 300 of original trout left?
5) The hot bowl of soup cools according to Newton's law of cooling. Temperature (in degrees Fahrenheit) at time t is provided by T(t) = 68+144e^-0.4t , where t is given in minutes.
i. Find the initial temperature of the soup?
ii. temperature of soup after 15 minutes?
c. How long after serving is soup 125°F?
6) Number of people in the town of 10,000 who have heard the rumor started by the few group of people is given by given function:
N(t) = 10000/5+1245e^-.97t
a. Find how many people were in group which began the rumor?
b. Find how many people have heard rumor after one day? After five days?
c. Find how long will it be until 1,000 of people in town have heard the rumor?