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Major Premise
“Biology will do for mathematics in the twenty-first century what physics did for mathematics in the twentieth century”
Major Premise
Almost all math and bio projects start at the calculus level or above.
But the overwhelming majority of beginning biology students, both majors and non-majors, typically are at the college algebra or precalculus level.
Most of these students have avoided math as much as possible.
Our Project
Our original plan was to begin developing the first stages of a new mathematics curriculum to serve the needs of biology students, both the bioscience majors and the non-majors.This would also impact the level of quantitative work in the biology courses.
Our Project
The project is a collaborative effort between Farmingdale State University and Suffolk Community College.Farmingdale State brings an exceptional history of successful efforts in reforming the mathematics curriculum.Suffolk brings an outstanding record of utilizing technology and quantitative methods in its introduction biology courses and labs.
The Farmingdale State Project
Our first step was to develop an alternative to our modeling-based precalculus course that would focus almost exclusively on biological applications. The course would feature a lab component taught by the biology faculty, so that each week’s primary math topic would be accompanied by an experiment requiring the use of that mathematical method.
Course TopicsWeek 1 Behavior of Functions Intro to Measurements
and Measuring
Week 2 Families of Functions,
Linear Functions
Linear Growth – part 1
Week 3 Linear Functions
and Linear Regression
Linear Growth – part 2
Week 4 Exponential Growth
and Decay Functions
Exponential Growth
Week 5 Exponential Regression
and Power Functions
Exponential Decay
part 1
Week 6 Power Functions and
Polynomials
Exponential Decay –
part 2
Course TopicsWeek 7 New functions from Old Power Function growthWeek 8 Logistic and Surge
Functions
Logarithmic Functions
Week 9 Matrix Models and
Linear Systems
Logistic Growth
Week 10 Sinusoidal Functions and Periodic Behavior
Surge Functions
Week 11 Periodic Functions – part 2
Polynomial growth
Week 12 Probability Models Periodic BehaviorWeek 13 Probability Models and
Difference Equations
Probability Model
(genetics)
What Happened Next
To accommodate the lab component, we had to change the precalculus course from four to five credits.
Because of that and conflicts with other courses (intro chemistry), the biology students did not register for the course and it did not run.
What We’ve Done Instead
All the labs in the introductory biology course are in the process of being changed to dramatically increase the level of quantitative experience – the new labs will incorporate most of the labs intended to be part of the precalculus course. The math department has officially created a new four credit precalculus course to serve the needs of the biology students – the same math course, but no lab.
What We’ve Done Instead
The math department has created a new two-semester calculus sequence for biology students – it will emphasize concepts over manipulation and will stress biological applications.The math department has created a one-semester post-precalculus mathematical modeling in the biological sciences course for bioscience majors and applied math majors.
Identify each of the following functions (a) - (n) as linear, exponential, logarithmic, or power. In each case, explain your reasoning.
(g) y = 1.05x (h) y = x1.05
(i) y = (0.7)t (j) y = v0.7
(k) z = L(-½) (l) 3U – 5V = 14
(m) x y (n) x y
0 3 0
5
1 5.1 1
7
2 7.2 2
9.8
3 9.3 3
13.7
Some Sample Problems
Biologists have long observed that the larger the area of a region, the more species live there. The relationship is best modeled by a power function. Puerto Rico has 40 species of amphibians and reptiles on 3459 square miles and Hispaniola (Haiti and the Dominican Republic) has 84 species on 29,418 square miles.
(a) Determine a power function that relates the number of species of reptiles and amphibians on a Caribbean island to its area. (b) Use the relationship to predict the number of species of reptiles and amphibians on Cuba, which measures 44,218 square miles.
Some Sample Problems
The accompanying table and associated scatterplot give some data on the area (in square miles) of various Caribbean islands and estimates on the number species of amphibians and reptiles living on each.Island Area N
Redonda 1 3
Saba 4 5
Montserrat 40 9
Puerto Rico 3459 40
Jamaica 4411 39
Hispaniola 29418 84
Cuba 44218 76
0
20
40
60
80
100
0 15000 30000 45000
Area (square miles)
Num
ber o
f Spe
cies
(a) Which variable is the independent variable and which is the dependent variable?(b) The overall pattern in the data suggests either a power function with a positive power p < 1 or a logarithmic function, both of which are increasing and concave down. Explain why a power function is the better model to use for this data.(c) Find the power function that models the relationship between the number of species, N, living on one of these islands and the area, A, of the island and find the correlation coefficient. (d) What are some reasonable values that you can use for the domain and range of this function?(e) The area of Barbados is 166 square miles. Estimate the number of species of amphibians and reptiles living there.
The ocean temperature near New York as a function of the day of the year varies between 36F and 74F. Assume the water is coldest on the 40th day and warmest on the 224th. (a) Sketch the graph of the water temperature as a function of time over a three year time span.(b) Write a formula for a sinusoidal function that models the temperature over the course of a year.(c) What are the domain and range for this function?(d) What are the amplitude, vertical shift, period, frequency, and phase shift of this function?(e) Estimate the water temperature on March 15.(f) What are all the dates on which the water temperature is most likely 60?
