Exam 8: Exponential Astonishment

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growingsuburban town (based on a current population of 100,000). -Use the average growth rate between 1850 and 1950, which was about 2.6%.

Use the pH scale to answer the question. -If the pH of a solution decreases by 1.6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic?

Provide an appropriate response. -The current population of a threatened animal species is 1 million, but it is declining with a half-life of 27 years. How many animals will be left in 74 years?

Provide an appropriate response. -_______ growth occurs when a quantity grows by the same relative amount in each unit of time.

Provide an appropriate response. -Money in a bank account earning compound interest at an annual percentage rate of 3% represents an example of linear growth.

Provide an appropriate response. -Given that $\log _ { 10 } 2 = 0.301$ , find $\log _ { 10 } 16$ without using a calculator.

Provide an appropriate response. -Earthquake strength is described in decibels, the loudness of sounds is described in pH, and the acidity of household cleansers is described by magnitudes.

Provide an appropriate response. -The carrying capacity is the largest population the environment can support for extended periods of time.

Provide an appropriate response. -Exponential growth cannot continue indefinitely. After only a relatively large number of doublings, exponentially growing quantities reach possible proportions.

Provide an appropriate response. -Consider a population that begins growing exponentially at a base rate of 2% per year and then follows a logistic growth pattern. If the carrying capacity is 41 million, find the actual growth rate When the population is 14 million.

Provide an appropriate response. - $10 ^ { - 0.874 }$ is between 0 and 1.

Use the decibel scale to answer the question. -What is the loudness, in decibels, of a sound 16 trillion times as loud as the softest audible sound?

Provide an appropriate response. -The initial population of a town is 16,237 and it grows with a doubling time of 24 years. What will the population be in 2 years?

Provide an appropriate response. -Suppose a population has a doubling time of 40 years. By what factor will it grow in 40 years?

Provide an appropriate response. -A certain radioactive isotope decays at a rate of 0.15% per year. Determine the half-life of this isotope, to the nearest year.

Determine whether the growth (or decay)is linear or exponential, and answer the associated question. -The value of your house is rising by $24,731 per year. If it is worth $199,401 today, what will it be worth in three years?

Provide an appropriate response. -Use the growth rate of 0.7% to estimate the population of a growing country in 2072. Start from the 2000 population of 50 million. Use the approximate doubling time formula.

Use the pH scale to answer the question. -What is the hydrogen ion concentration of a solution with pH 2.5?

Provide an appropriate response. -If you decrease the amount of water in the cup, you'll decrease the pH of the water in the cup.

Provide an appropriate response. -Poaching is causing a population of elephants to decline by 6% per year. Use the approximate half-life formula to determine the fraction that remains in 76 years if there are 13,365 elephants Today.