Answer:
The best prediction for the population in year 25 is
Step-by-step explanation:
we have a exponential function of the form
where
a is the initial value
b is the base
In this problem
so
For
substitute
Round up
James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The
1 answer:
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F(x) = 4x - 1
g(x) = 2x² + 3
1. (f + g)(x) = (4x - 1) + (2x² + 3)
(f + g)(x) = 2x² + 4x + (-1 + 3)
(f + g)(x) = 2x² + 4x + 2
Domain: {x| -∞ < x < ∞}, (-∞, ∞)
2. (f - g)(x) = (4x + 1) - (2x² + 3)
(f - g)(x) = 4x + 1 - 2x² - 3
(f - g)(x) = -2x² + 4x + 1 - 3
(f - g)(x) = -2x² + 4x - 2
Domain: {x|-∞ < x < ∞}, (-∞, ∞)
3. (g - f)(x) = (2x² + 3) - (4x - 1)
(g - f)(x) = 2x² + 3 - 4x + 1
(g - f)(x) = 2x² - 4x + 3 + 1
(g - f)(x) = 2x² - 4x + 4
Domain: {x| -∞ < x < ∞}, (-∞, ∞)
4. (f · g)(x) = (4x + 1)(2x² + 3)
(f · g)(x) = 4x(2x² + 3) + 1(2x² + 3)
(f · g)(x) = 4x(2x²) + 4x(3) + 1(2x²) + 1(3)
(f · g)(x) = 8x³ + 12x + 2x² + 3
(f · g)(x) = 8x³ + 2x² + 12x + 3
Domain: {x| -∞ < x < ∞}, (-∞, ∞)
5.
Domain: 2x² + 3 ≠ 0
- 3 - 3
2x² ≠ 0
2 2
x² ≠ 0
x ≠ 0
(-∞, 0) ∨ (0, ∞)
6.
Domain: 4x - 1 ≠ 0
+ 1 + 1
4x ≠ 0
4 4
x ≠ 0
(-∞, 0) ∨ (0, ∞)
g(x) = 2x² + 3
1. (f + g)(x) = (4x - 1) + (2x² + 3)
(f + g)(x) = 2x² + 4x + (-1 + 3)
(f + g)(x) = 2x² + 4x + 2
Domain: {x| -∞ < x < ∞}, (-∞, ∞)
2. (f - g)(x) = (4x + 1) - (2x² + 3)
(f - g)(x) = 4x + 1 - 2x² - 3
(f - g)(x) = -2x² + 4x + 1 - 3
(f - g)(x) = -2x² + 4x - 2
Domain: {x|-∞ < x < ∞}, (-∞, ∞)
3. (g - f)(x) = (2x² + 3) - (4x - 1)
(g - f)(x) = 2x² + 3 - 4x + 1
(g - f)(x) = 2x² - 4x + 3 + 1
(g - f)(x) = 2x² - 4x + 4
Domain: {x| -∞ < x < ∞}, (-∞, ∞)
4. (f · g)(x) = (4x + 1)(2x² + 3)
(f · g)(x) = 4x(2x² + 3) + 1(2x² + 3)
(f · g)(x) = 4x(2x²) + 4x(3) + 1(2x²) + 1(3)
(f · g)(x) = 8x³ + 12x + 2x² + 3
(f · g)(x) = 8x³ + 2x² + 12x + 3
Domain: {x| -∞ < x < ∞}, (-∞, ∞)
5.
Domain: 2x² + 3 ≠ 0
- 3 - 3
2x² ≠ 0
2 2
x² ≠ 0
x ≠ 0
(-∞, 0) ∨ (0, ∞)
6.
Domain: 4x - 1 ≠ 0
+ 1 + 1
4x ≠ 0
4 4
x ≠ 0
(-∞, 0) ∨ (0, ∞)
Answer:
The histogram of the data is attached below.
Step-by-step explanation:
A histogram is a demonstration of statistical data that uses bars to illustrate the incidence of data values in successive numerical intervals of same size. In the most basic form of histogram, the independent variable is marked along the x-axis and the dependent variable is marked along the y-axis.
The data provided is:
X Frequency
1 12
2 3
3 7
4 9
5 18
6 14
The histogram of the data is attached below.
