Answer:
Step-by-step explanation:
you need to draw a leaf plot
Answer:
17.34 years
Step-by-step explanation:
The equation you wrote in the first part of the problem can be solved for the value of t that makes the population be 5000.
![P(t)=\dfrac{10000}{1+11.5e^{-0.1408614477t}}](https://tex.z-dn.net/?f=P%28t%29%3D%5Cdfrac%7B10000%7D%7B1%2B11.5e%5E%7B-0.1408614477t%7D%7D)
Setting this equal to 5000 and multiplying by the denominator, we have ...
![5000=\dfrac{10000}{1+11.5e^{-0.1408614477t}}\\\\5000+57500e^{-0.1408614477t}=10000\\\\e^{-0.1408614477t}=\dfrac{5000}{57500}\qquad\text{subtract 5000, divide by 57500}\\\\-0.1408614477t = \ln{\dfrac{1}{11.5}}=-\ln(11.5)\qquad\text{take logs}\\\\t=\dfrac{\ln(11.5)}{0.1408614477}\approx17.3386](https://tex.z-dn.net/?f=5000%3D%5Cdfrac%7B10000%7D%7B1%2B11.5e%5E%7B-0.1408614477t%7D%7D%5C%5C%5C%5C5000%2B57500e%5E%7B-0.1408614477t%7D%3D10000%5C%5C%5C%5Ce%5E%7B-0.1408614477t%7D%3D%5Cdfrac%7B5000%7D%7B57500%7D%5Cqquad%5Ctext%7Bsubtract%205000%2C%20divide%20by%2057500%7D%5C%5C%5C%5C-0.1408614477t%20%3D%20%5Cln%7B%5Cdfrac%7B1%7D%7B11.5%7D%7D%3D-%5Cln%2811.5%29%5Cqquad%5Ctext%7Btake%20logs%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B%5Cln%2811.5%29%7D%7B0.1408614477%7D%5Capprox17.3386)
For the population to reach 5000, it will take about 17.34 years.
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<em>Additional comment</em>
The value -0.14086... is the natural log of the ratio 1818/2093. This means the "exact answer" is ln(11.5)/(ln(2093) -ln(1818)), an irrational number.
A graphing calculator can answer the question easily.
The volume of a cone is given by the formula
![V=\frac{1}{3} \pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h)
, where <em>r</em> is the radius and <em>h</em> is the height. The horizontal dotted line from the center of the base circle to the outside edge would be the radius, so that would be 12 cm. The vertical dotted line from the center of the base to the point of the cone would be the height, so that would be 8 cm. We substitute these values into our formula:
![V=\frac{1}{3} \pi (12^2)(8)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%2812%5E2%29%288%29)
Substituting 3.14 for pi we have:
Answer:
35 times
Step-by-step explanation:
60x + 480 = 2580
60x = 2100
x = 35