Race track principle says that if two functions are equal at <span>t=0</span>, then the one which has a greater derivative will be greater.
In this case we're comparing <span><span>f′</span>(t)</span> and <span><span>g′</span>(t)</span>. So we make sure that <span>g(0)=<span>f′</span>(0)</span> and that <span><span>f′′</span>(t)≥<span>g′</span>(t)
</span>
<span>g(t)=at+b</span>
Since it is a line.
<span><span>g′</span>(t)=a</span>
<span><span>f′′</span>(t)≥3≥<span>g′</span>(t)⟹3≥a</span>
So let <span>a=3</span>.
<span><span>f′</span>(0)=0=g(0)=3(0)+b⟹b=0
</span>So that means
<span>g(t)=3t
</span>Do something similar for <span>h(t)</span><span> starting with
</span><span>h(t)=a<span>t2</span>+bt+c
</span><span>h(0)=f(0)⟹c=0
</span>
So
<span>h</span><span>(</span><span>t</span><span>)</span><span>=</span><span>a</span><span>t2</span><span>+</span><span>b</span><span>t</span>
Answer:
The 95% confidence interval is ( 27.126 , 34.674)
Step-by-step explanation:
Given
The t critical value at 0.05 level = 2.023 for the df = 39
Confidence interval = 95%
Mean
Substituting the given values we get -
Hence, the 95% confidence interval is
( 27.126 , 34.674)
Answer:
The population in 2003 was 234 million
Step-by-step explanation:
In order to calculate the population in 2003 we would have to use the The exponential growth formula as follows:
p(y)=ir^t
According to the given data:
p(y)=233 million
i=231 million
t
=1999-1991
Therefore, 233 million=231 million r^(1999-1991)
(233 million/231 million)^(1/8)=r
p(y)=231 million(233 million/231 million)^((y-1991)/8)
Therefore, in 2003
p(2003)=231 million(233 million/231 million)^((2003-1991)/8)
p(2003)=231 million(233 million/231 million)^(1.5)
p(2003)=234 million
The population in 2003 was 234 million
Answer:
y = x+5
Step-by-step explanation:
you cant times it by anything but 1 so x then how much does it go up by 5 so y= x+5
Answer:
slope of the parallel line = 8
Step-by-step explanation:
Parallel lines have the same slope. To determine the equation of the other line, you need to transform the given linear equation into its slope-intercept form, y = mx + b:
-8x + y = 2
Add 8x to both sides to isolate y:
-8x + 8x + y = 8x + 2
y = 8x + 2 (this is the slope-intercept form where the slope (m) = 8, and the y-intercept (b) = 2).
Given that the slope of the first equation is 8, then we can assume that the slope of line parallel to -8x + y = 2 will also be 8.
