Use a calculator with a y x key or a ∧ key to solve Exercises 65-70. India is currently one of the world's fastest-growing countries. By 2040, the population of India will be larger than the population of China; by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function f(x) ⋅ ⋅ 574(1.026) r models the population of India, f(x) . in millions, x years after 1974. a. Substitute 0 for x and, without using a calculator, find India’s population in 1974. b. Substitute 27 for x and use your calculator to find India's population, to the nearest million, in the year 2001 as modeled by this function. c. Find India’s population, to the nearest million, in the year 2028 as predicted by this function. d. Find India's population, to the nearest million, in the year 2055 as predicted by this function. c. What appears to be happening to India's population every 27 years?
Use a calculator with a y x key or a ∧ key to solve Exercises 65-70. India is currently one of the world's fastest-growing countries. By 2040, the population of India will be larger than the population of China; by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function f(x) ⋅ ⋅ 574(1.026) r models the population of India, f(x) . in millions, x years after 1974. a. Substitute 0 for x and, without using a calculator, find India’s population in 1974. b. Substitute 27 for x and use your calculator to find India's population, to the nearest million, in the year 2001 as modeled by this function. c. Find India’s population, to the nearest million, in the year 2028 as predicted by this function. d. Find India's population, to the nearest million, in the year 2055 as predicted by this function. c. What appears to be happening to India's population every 27 years?
Solution Summary: The author explains how to calculate the population of India in 1974 when the function for increase in population after x years from 1974 is f(x)=574
Use a calculator with a
y
x
key or a
∧
key to solve Exercises 65-70.
India is currently one of the world's fastest-growing countries. By 2040, the population of India will be larger than the population of China; by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function f(x)
⋅
⋅
574(1.026)r models the population of India, f(x). in millions, x years after 1974.
a. Substitute 0 for x and, without using a calculator, find India’s population in 1974.
b. Substitute 27 for x and use your calculator to find India's population, to the nearest million, in the year 2001 as modeled by this function.
c. Find India’s population, to the nearest million, in the year 2028 as predicted by this function.
d. Find India's population, to the nearest million, in the year 2055 as predicted by this function.
c. What appears to be happening to India's population every 27 years?
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Does the series converge or diverge
Chapter 3 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)
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