91Ó°ÊÓ

Suppose a country's population increases by a total of \(6 \%\) over a three- year period. What is the continuous growth rate for this country?

Suppose a colony of bacteria has a continuous growth rate of \(40 \%\) per hour. If the colony contains 7500 cells now, how many did it contain three hours ago?

A colony of bacteria is growing exponentially, doubling in size every 100 minutes. How many minutes will it take for the colony of bacteria to triple in size?

Suppose a colony of bacteria has a continuous growth rate of \(35 \%\) per hour. How long does it take the colony to triple in size?

P Suppose a colony of bacteria starts with 200 cells and triples in size every four hours. (a) Find a function that models the population growth of this colony of bacteria. (b) Approximately how many cells will be in the colony after six hours?

Suppose \(\$ 700\) is deposited in a bank account paying \(6 \%\) interest per year, compounded 52 times per year. How much will be in the bank account at the end of 10 years?

Suppose \(\$ 8000\) is deposited in a bank account paying \(7 \%\) interest per year, compounded 12 times per year. How much will be in the bank account at the end of 100 years?

Suppose a bank wants to advertise that \(\$ 1000\) deposited in its savings account will grow to \(\$ 1050\) in one year. This bank compounds interest 365 times per year. What annual interest rate must the bank pay?

Find three newspaper articles that use the word "exponentially" (one way to do this is to use the web site of a newspaper that allows searches). For each use of the word "exponentially" that you find in a newspaper article, discuss whether or not the word is used in its correct mathematical sense.

Suppose you whisper at 20 decibels and normally speak at 60 decibels. (a) Find the ratio of the sound intensity of your normal speech to the sound intensity of your whisper. (b) Your normal speech seems how many times as loud as your whisper?