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 Subject: Calculus I Problem Category: Science > Math Asked by: wannabeleader-ga List Price: \$3.00 Posted: 11 Jul 2005 15:18 PDT Expires: 10 Aug 2005 15:18 PDT Question ID: 542336
 ```The population, P, of China, in billions, can be approximated by the function: P=1.15(1.014)^t Where t is the number of years since the start of 1993. According to this model, how fast is the population growing at the start of 1993 and at the start of 1995? Give your answers in millions of people per year. I need this done in a detailed write up, explaining each step.```
 ```Hello wannabeleader! In order to find the answer, we must take the derivative of the function you provide with respect to t. Recall that the derivative shows by how much the function is changing when the variable you're deriving with respect to (t, in this case) increases one unit (in this case, one unit is one year). We have that: P = 1.15*(1.014)^t The derivative of this function is: dP/dt = 1.15*ln(1.014)*(1.014)^t = (If you don't know how to calculate a derivative, the following link might help) Mathwords: Derivative Rules http://www.mathwords.com/d/derivative_rules.htm Now we just need to plug the appropiate values of t in the derivative to get the answer. At the start of 1993, we are zero years from the start of 1993; thus t=0. Plugging t=0, we get: dP/dt = 1.15*ln(1.014)*(1.014)^0 = 0.0159883... Since this value is in billions, we get that the population grows at 15.98 million people per year at the start of 1993. At the beginning of 1995, t=2. So dP/dt = 1.15*ln(1.014)*(1.014)^2 = 0.01643914... Again, this means that the population grows at 16.43 million people per year at the start of 1995. I hope this helps! Best wishes, elmarto``` Request for Answer Clarification by wannabeleader-ga on 12 Jul 2005 08:10 PDT ```I do have one quick question, which deriviative rule did you use to find the equation ?``` Clarification of Answer by elmarto-ga on 12 Jul 2005 11:52 PDT ```Hello, Thanks for the rating and tip! Regarding your question, I used rule 12 in the link I provided; that is, the derivative of exponential functions. Best regards, elmarto```
 wannabeleader-ga rated this answer: and gave an additional tip of: \$1.00 ```Thank you so much! I have a couple other math problems on here from a quiz if you wanna help me out that would be great.```