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How do I write an exponential function based on this information?

How do I write an exponential function based on this information? Topic: How to write an exponential function
June 19, 2019 / By Delphia
Question: In 1900 the population of a town was 5000. The population increased at an average rate of 2.5% per year. What was the population in 1920? Okay, now what is the equation that I need to use? If I get the formula I can figure it out if you tell me what variables represent what constant. Thanks!
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Best Answers: How do I write an exponential function based on this information?

Caetlin Caetlin | 5 days ago
P = Po(1+r/100)^n = Po(1+i)^n where P= Present Population= Population on 1920 Po = Population in 1900= 5000 r = 2.5 % i = 2.5/100= 0.025 n = number of years P = 5000{1.025)^20= = 8193........................Ans
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Caetlin Originally Answered: In Algebra 2, how do you write a log function into an exponential function if it doesn't have the "b" variable?
Log is understood to have a base of ten unless otherwise specified. this equation in exponential form is 10^1=10 ...... so 10=10 so the log of ten is 1. Hope this helps
Caetlin Originally Answered: In Algebra 2, how do you write a log function into an exponential function if it doesn't have the "b" variable?
How do I write a function B(l) that represents the portion of the rectangle with length l provided that the fringe of the aforementioned rectangle is 100 and twenty feet? 2(l + B) = 100 and twenty l + B = 60 B(l) = l(60 - l) A = 60l - l^2 Use B(l) to discover the dimensions of the rectangle. a. 500 feet^2 500 = 60l - l^2 b. seven hundred feet^2 seven hundred = 60l - l^2 Why is a community of one thousand feet^2 not accessible? 1000 = 60l - l^2

Almah Almah
The Population Function is given by P(x) = 5000(0.025x + 5000) P(x) = 5000(0.025x + 1) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ where P = population and x = no. of years y1 = 1900 y2 = 1920 x = y2 - y1 x = 1920 - 1900 x = 20 P(20) = 5000(0.025(20) + 1) P(20) = 5000(0.5 + 1) P(20) = 5000(1.5) P(20) = 7500 The population in 1920 was 7500. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
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Val Val
P = Pi*e^(rt) ...where: P= current at time t1 Pi = initial population e = 2.718 r = rate of growth t = time
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Val Originally Answered: How do you write the exponential function using the given points? (1,20) (2,4)?
The form of an exponential function is y = ab^x. So if we substitute for x and y we get two equations and two unknowns: 20 = ab^1 4 = ab^2 We can eliminate a by dividing the two equations: 5 = b^(1-2) Solve for b: 5 = b^(-1). 5 = 1/b; b = (1/5). Now substitute into either equation to get the constant a. I'll use the top one: 20 = a(1/5)^1 Solve for a: 20 = a(1/5); a = 100. So the function is f(x) = 100*(1/5)^x. To check, f(1) = 100*(1/5)^1 = 100/5 = 20. f(2) = 100*(1/5)^2 = 100/25 = 4. Note that f(x) can also be written: f(x) = 100*5^-x. Strictly speaking, the mathematical term "exponential function" refers to the use the base of the natural log, e. We can do that here, but the exponent of e will have -ln5 as the coefficient of x. The constant a will not change.

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