- 7.4.1: A population of protozoa develops with a constant relative growth r...
- 7.4.2: A common inhabitant of human intestines is the bacterium Escherichi...
- 7.4.3: A bacteria culture initially contains 100 cells and grows at a rate...
- 7.4.4: A bacteria culture grows with constant relative growth rate. The ba...
- 7.4.5: The table gives estimates of the world population, in millions, fro...
- 7.4.6: The table gives the population of India, in millions, for the secon...
- 7.4.7: Experiments show that if the chemical reaction N2O5 l2NO2 1 2O2 tak...
- 7.4.8: Strontium-90 has a half-life of 28 days. (a) A sample has a mass of...
- 7.4.9: The half-life of cesium-137 is 30 years. Suppose we have a 100-mg s...
- 7.4.10: A sample of tritium-3 decayed to 94.5% of its original amount after...
- 7.4.11: Scientists can determine the age of ancient objects by the method o...
- 7.4.12: A curve passes through the point and has the property that the slop...
- 7.4.13: A roast turkey is taken from an oven when its temperature has reach...
- 7.4.14: In a murder investigation, the temperature of the corpse was at 1:3...
- 7.4.15: When a cold drink is taken from a refrigerator, its temperature is ...
- 7.4.16: A freshly brewed cup of coffee has temperature C in a C room. When ...
- 7.4.17: The rate of change of atmospheric pressure with respect to altitude...
- 7.4.18: (a) If $1000 is borrowed at 8% interest, nd the amounts due at the ...
- 7.4.19: (a) If $3000 is invested at 5% interest, nd the value of the invest...
- 7.4.20: (a) How long will it take an investment to double in value if the i...
- 7.4.21: Consider a population with constant relative birth and death rates ...
- 7.4.22: Let be a positive number. A differential equation of the formwhere ...
Solutions for Chapter 7.4: EXPONENTIAL GROWTH AND DECAY
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) | 4th Edition
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)
An interval that includes its endpoints
Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)
Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)
A statement that describes a bounded interval, such as 3 ? x < 5
Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.
Point where a curve crosses the x-, y-, or z-axis in a graph.
See Polynomial function in x
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative
Linear regression equation
Equation of a linear regression line
The line segment through the foci of an ellipse with endpoints on the ellipse
Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)
A square matrix with nonzero determinant
The graph of parametric equations.
Projection of u onto v
The vector projv u = au # vƒvƒb2v
Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator
A number that measures a quantitative variable for a sample from a population.
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.
See n factorial.