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Pavlova-9 [17]
4 years ago
10

The population of a city is growing according to the exponential model p = cekt, where p is the population in thousands and t is

measured in years. if the population doubles every 11 years what is k, the city's growth rate? [round answer to the nearest hundredth.]
a.2.8%
b.4.4%
c.6.3%
d.8.9%
Mathematics
2 answers:
kipiarov [429]4 years ago
7 0

Answer: C. 6.3%

Step-by-step explanation:

Anarel [89]4 years ago
5 0
P = ce^(kt)
make p = 2c because doubling will be
like c-->2c, so if p = 2c, then
p = ce^(kt)
2c = ce^(kt)
2c/c = (ce^(kt))/c
2 = e^(kt)
Now take natural logarithm (ln) of both sides of the equation:
ln (2) = ln (e^(kt))
0.693 = kt×ln e
**this is because ln of an exponent makes the exponent become multiplied by the ln,
and ln e = 1
0.693 = kt×ln e
0.693 = kt×1, and t = 11 years
0.693 = k(11)
0.693/11 = 11k/11
k = 0.063, multiply by 100 to get %
k = 6.3%
answer is C
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<h3>Solution</h3>

First of all, look at how this is evaluated in terms of what happens to a value for s.

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Note that the division is of everything on both sides of the equation. That is why we need to add parentheses around the expression that was on the left—so the whole thing gets divided by 2.

Your solution is ...

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Answer:

a) y=0.00991 x +1.042  

b) r^2 = 0.7503^2 = 0.563

c) r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

y = mx +b

Wehre

m=\frac{S_{xy}}{S_{xx}}  

And:  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}  

With these we can find the sums:  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=2595100-\frac{4210^2}{7}=63085.714  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625  

And the slope would be:  

m=\frac{625}{63085.714}=0.00991  

Nowe we can find the means for x and y like this:  

\bar x= \frac{\sum x_i}{n}=\frac{4210}{7}=601.429  

\bar y= \frac{\sum y_i}{n}=\frac{49}{7}=7  

And we can find the intercept using this:  

b=\bar y -m \bar x=7-(0.00991*601.429)=1.042  

And the line would be:

y=0.00991 x +1.042  

Part b

The correlation coefficient is given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=7 \sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354  

r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

The determination coefficient is given by:

r^2 = 0.7503^2 = 0.563

Part c

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