- 9.4.1: A population of protozoa develops with a constant relative growth r...
- 9.4.2: A common inhabitant of human intestines is the bacterium Escherichi...
- 9.4.3: A bacteria culture starts with 500 bacteria and grows at a rate pro...
- 9.4.4: A bacteria culture grows with constant relative growth rate. After ...
- 9.4.5: The table gives estimates of the world population, in millions, fro...
- 9.4.6: The table gives the population of the United States, in millions, f...
- 9.4.7: Experiments show that if the chemical reaction takes place at , the...
- 9.4.8: Bismuth-210 has a half-life of 5.0 days. (a) A sample originally ha...
- 9.4.9: The half-life of cesium-137 is 30 years. Suppose we have a 100-mg s...
- 9.4.10: After 3 days a sample of radon-222 decayed to 58% of its original a...
- 9.4.11: Scientists can determine the age of ancient objects by a method cal...
- 9.4.12: A curve passes through the point and has the property that the slop...
- 9.4.13: A roast turkey is taken from an oven when its temperature has reach...
- 9.4.14: A thermometer is taken from a room where the temperature is C to th...
- 9.4.15: When a cold drink is taken from a refrigerator, its temperature is ...
- 9.4.16: A freshly brewed cup of coffee has temperature C in a C room. When ...
- 9.4.17: The rate of change of atmospheric pressure with respect to altitude...
- 9.4.18: (a) If $500 is borrowed at 14% interest, find the amounts due at th...
- 9.4.19: (a) If $3000 is invested at 5% interest, find the value of the inve...
- 9.4.20: (a) How long will it take an investment to double in value if the i...
- 9.4.21: Consider a population with constant relative birth and death rates ...
- 9.4.22: Let be a positive number. A differential equation of the form where...
Solutions for Chapter 9.4: Exponential Growth and Decay
Full solutions for Calculus, | 5th Edition
A matrix whose elements are the coefficients in a system of linear equations
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
Inverse sine function
The function y = sin-1 x
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a
Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)
See Numerical derivative of ƒ at x = a.
The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space
An equation in r and ?.
A statistical measure that does not change much in response to outliers.
A logarithmic scale used in measuring the intensity of an earthquake.
A transformation that leaves the basic shape of a graph unchanged.
Sample standard deviation
The standard deviation computed using only a sample of the entire population.
A line that is neither horizontal nor vertical
Standard position (angle)
An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive x-axis
Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,
Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)
Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.
The square of the standard deviation.
Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.