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The population of a southem city follows the exponential Iaw H the population doubled in size over 22 months and the current population is 10,000,what wl the popu...

Question

The population of a southem city follows the exponential Iaw H the population doubled in size over 22 months and the current population is 10,000,what wl the population be 2 years from now? What will the population be 2 years from now?The population will be approximately people (Do not round unti the final answer Then round to Ihe nearest whole number as needed )

The population of a southem city follows the exponential Iaw H the population doubled in size over 22 months and the current population is 10,000,what wl the population be 2 years from now? What will the population be 2 years from now? The population will be approximately people (Do not round unti the final answer Then round to Ihe nearest whole number as needed )



Answers

Population Growth The population of a southern city follows the exponential law. (a) If $N$ is the population of the city and $t$ is the time in years, express $N$ as a function of $t .$ (b) If the population doubled in size over an 18 -month period and the current population is $10,000,$ what will the population be 2 years from now?

So we are asked to find the function in terms of T. Where we have an exponential law model and that would be A and tears and years. So be says in 18 months the population doubled. Well, that's what's going to give us the K. value for this particular population. So if the population double, that means you can pick whatever you want for N. But I'm gonna keep it is and zero E. To the K. And time would be 1.5 persistent years. And then I want that population to double. So right here, that's all I'm using. So I can find K. So that gives me two equals E. To the 1.5 K. And we're gonna find K. So the natural log of two equals 1.5 K. Or K equals the natural log of two Divided by 1.5. So let's figure that out. A natural lock of two Divided by 1.5. So we know K Eagles .462. We're going to use that for this question right here. So we're using the same formula. The current population is 10,000. Okay. We figured out to be 462 for this area, and we want it two years from now. What will the new population be? So we're going to do 10,000 b. raised to the Wait a full 6 2 times two. So our new population is 25,193.

In this scenario, we have a city and were asked to create a function for the population where Tisa population and t where Ennis the population to use the time of years so we can come up with the general formula for the logistic population growth or exponential. So end of teas A total population is equal to starting population and zero times he raised to the K T power where K is ah is a rate in decimal of the decay or growth um, ends. He is time for part B where told that were given information that the population doubles over 18 month period and the current population is 10,000. So if it doubled, that means the starting population must have been 5000. So 5000 is and zero They were doing something e to the K. Uh, and he, in this case is equal to a warty is time of years and were given 18 month period so that that is 1.5 years to resolve in four K. Over here divide both sides by 5000. We get two is equal to you to the Kate 1.5 k Take the natural log both sides. We have 1.5 k sequel to two and divide to buy 1.5 or divide both sides by 1.5. We have one, um, 0.33 So K is equal to approximately 1.33 repeating. You just keep it simple And where, as he used this value of K of the increase of the growth, um, been the population in two years, basically. So we want to find out of T where n is one of zeros cut the same 5000 times E k times to the race, like through 1.33 times two. So here we could just put this all into a calculator. So 5000 times e to the 1.33 times, um, times to power is equal to approximately 7 71,481 And this is rounding to the nearest whole number because we're trying to find a number of people. So just leave our answer here

The population of the town increases 4.2% in one year. If the original population was 19,500 what's the population after the increase? Using the one step method, that means I'm taking 100% off the population, and I'm adding 4.2%. So that means I'm actually finding 100 and 4.2% off my original, so I'm gonna put 100 4.2 as my percent. So that means I'm looking for the part. And the original was 19,000 500. So 100 a is going to be 104 point fat. I'm sorry. Point to times 19,500 and that's gonna be 2,031,900. So when I divide by 100 I'm gonna get 20,000 319

It's a problem. We are given the initial population off the city in 2000 eighties 50,000 and the growth rate is 4.5%. So first, let's convert this into decimal number, which is zero boys, you know, 45 and part A. We need to give the population of the CD as a function of time. We seize in years, so we have peace up. T equal to piece of zero is 50,000 times e to the R t. So this is grow gray. So are is a positive number which is 0.0 45 t and then we have two sketches, so grab. So since the initial population is 50,000 so t equal to zero here we have peace of tea is 50,000 and then the population is growing, so aren't grab will look like this and part B, we have 25 the population in 2018. So since we start 2008 so 2018 which mean 10 years after we have peace of 10 equal to 50,000 times e to those zero poise, it'll 45 times 10. So these key me 7 8115 46 sayings the population has to be in the imager. So this is I'm gonna rabbit out to 78,416 Farsi is We have to, fi, um, how many years the population will reach 100,000 so we can ask tothis equation. What? He So we have 100,000 equal to 50,000 e to the 0.0 45 t So we want to isolate the tea by divided both side by 50 1000 and then I got to equal to eat the 0.0 45 t. So, in order to bring this dow here, I'm going to take the natural up on both sides. So I have national lock to equal to natural law off Spee to the zero poison or 45 t. So I have national off two equals 20 boys. It'll 45 t and then divide both sides by 0.0 45 to so 40. So I got TA is approximately 15 44 years. So in 15.4 years the population will reach 100,000


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