Exponential growth word problem (Algebra 2/Trig):?

Question

The population of Indonesia was 191,256,000 in 1990 and was growing at a rate of 1.9% per year. Predict the population, to the nearest hundred thousand of Indonesia in 2010.

Answer 1

Take the starting number, and multiply by (1.019)^20.

To see why that's true, convince yourself that the population any year is 1+.019 = 1.019 times what it was the prior year.

Then convince yourself that the population after two years is 1.019^2 times what it was the first year.

Then generalize. :)

Answer 2

f(t) = C*(one million-r)^t think of of (r) as a value of deterioration (observe which you may have an exponential strengthen: purely replace (one million+r) for (one million-r)). in many situations, "r" is between 0 and one million so (one million-r) is between 0 and one million. They enable you recognize the cost of deterioration is seventy 5% so (one million-r) = (one million-.seventy 5) so the decay consistent is (.25) "t" might properly be acknowledged as time if the equation replace into modeling decay vs time. because of the fact your equation fashions the variety of contestants and the cost of deterioration is with admire to each around (word you have been given the decay ingredient "in each and every around" it incredibly is "consistent with around") your "t" might properly be acknowledged because of the fact the variety of rounds because of the fact around 0. to evaluate the habit of the functionality enable t=0. At t=0 i.e., around 0, there are C contestants -- is clever because of the fact no person is eradicated on the beginning up of the competition. f(t) = y has the contraptions of C because of the fact (one million-r)^t is completely a relentless that relies upon on the around. because of the fact C represents the variety of contestants, f(t) additionally represents the variety of contestants. you're finding for f(t) = one million. one million = 4096(.25)^t you're fixing for t. ln(one million/4096) = ln(.25^t) = t*ln(.25) ln(one million/4096)/ln(.25) = t t = 6 Woops. the guy decrease than has the translation of cost of deterioration maximum dazzling. cost of deterioration is "r". The decay consistent is (one million-r) compounded "t" situations