Answer:
Part 1. 0.9259 % per year
Part 2. P = 281.4e^(0.009 259t); 338.6 million
Step-by-step explanation:
Data:
P₀ = 281.4 million
P = 308.7 million
Part 1. Growth rate
t = 2010 - 2000 = 10 yr
P = P₀e^(rt)
308.7 = 281.4e^(10r)
e^(10r) = 1.0970
10r = ln1.0970
r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259
r = 0.9259 % per year
The 10-year continuous growth rate is 0.9259 % per year.
Part 2. Population model
The population model is
P = 281.4e^(0.009 259t)
where P is in millions and t is the number of years since 2000.
By 2020,
P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203
P = 338.6 million
The estimated population in 2020 is 338.6 million.
By normal curve symmetry
<span>from normal table </span>
<span>we have z = 1.15 , z = -1.15 </span>
<span>z = (x - mean) / sigma </span>
<span>1.15 = (x - 150) / 25 </span>
<span>x = 178.75 </span>
<span>z = (x - mean) / sigma </span>
<span>-1.15 = (x - 150) / 25 </span>
<span>x = 121.25 </span>
<span>interval is (121.25 , 178.75) </span>
<span>Pr((121.25-150)/25 < x < (178.75-150)/25) </span>
<span>is about 75%</span>
Length - l
Width - w
Given,
Perimeter = 60
2(l +w) = 60
l + w = 30
l = 30 - w
Given,
l = 3w
30 - w = 3w
4w = 30
--- w = 7.5
--- l = 3w = 3 * 7.5 = 29.5
Hence, the length of the rectangle is 29.5 and the width is 7.5
Answer:
It increases x3.
Step-by-step explanation:
Let's say the fraction to begin with was 100/100. Ignore the fact that it isn't fully reduced and it is an improper fraction.
10% of 100 is 10, so the numerator is now 90 (decrease=get smaller; 100-10=90).
70% of 100 is 70, so the denominator is now 30 (decrease=get smaller; 100-70=30).
Our fraction is now 90/30 which, when fully reduced, equals 3.00. Since 100/100 equals 1.00, it has increased by 2.00 (3x bigger).
