Overview
1. If you invest $5000 in a CD that pays 3% interest compounded continuously, how much interest will you earn over 8 years? Enter your value only; do not include units with the answer.
2-1. The amount of methane in the atmosphere (in parts of volume per billion) can be approximated by,
[Image unavailable: C left parenthesis t right parenthesis equals 715 e to the power of 0.00356 t end exponent space space left parenthesis p a r t s divided by b i l l i o n right parenthesis],
where t is the time in years since 1,750. Use the model to estimate the amount of methane (in parts per billion) in the atmosphere in 2050. Round answer to 1-decimal place and do not include units with the answer.
2-2. Continuing with the previous problem, after about how many years will it take for the quantity of methane in the atmosphere to double? Round answer to 1-decimal place and do not include units with the answer.
3-1. What is the value, [Image unavailable: f left parenthesis 2 right parenthesis], of the logistic function below? Round value to 3-decimal places.
[Image unavailable: f left parenthesis x right parenthesis equals fraction numerator 10 over denominator 1 plus 4 open parentheses 3 to the power of negative x end exponent close parentheses end fraction]
3-2. Continuing with the previous problem, at what x-value is the curve the steepest? Round value to 2-decimal places.
4-1. The U.S. population was 180 million in 1960 and 309 million in 2010. Find an exponential model for the population, P, of the U.S. in millions as a function of t, where t is the number of years since the start of 1960. SHOW WORK. Do work by hand on a piece of paper in ink and then upload a pdf of your work as your answer to this question.
4-2. Continuing with the previous problem, use your function to predict the U.S. population in the year 2025. SHOW WORK. Do work by hand on a piece of paper in ink and then upload a pdf of your work as your answer to this question.
5-1. There are currently 100 cases of flu in a small town of population 1,000 people, and all the people of the town are susceptible and will eventually get the flu. Early in the flu epidemic, the number of cases is increasing by 20% each day. Find a logistic function that gives the number, P, of people with the flu as a function of t, the number of days from now. SHOW WORK. Do work by hand on a piece of paper in ink and then upload a pdf of your work as your answer to this question. Your function should be in the form,
[Image unavailable: begin mathsize 16px style P left parenthesis t right parenthesis equals fraction numerator N over denominator 1 plus A left parenthesis b to the power of – t end exponent right parenthesis end fraction end style]
5-2. Continuing with the previous problem, how long will it take for the number of cases to reach 300? SHOW WORK. Do work by hand on a piece of paper in ink and then upload a pdf of your work as your answer to this question.