Find an exponential function to model the data below and use it to predict about

Question

Find an exponential function to model the data below and use it to predict about how many widgets will be produced in 2004. 20 million widgets 60 million widgets 41 million widgets 11 million widgets How long would it take $6, 000 to grow to $30, 000 at 5% compounded continuously? Round your answer to the nearest tenth of a year. 32.2 years 33.2 years 20.2 years 32.5 years The sales of a new model of notebook computer are approximated by the formula S(x) =5, 000 - 11, 000 e-x/8, where x represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how many months will the sales reach $1, 500, 000? 9 months 16 months 19 months 12 months A pair of rabbits are introduced on a small island, and the population grows until the food supply and natural enemies of the rabbits on the island limit the population. If the number of rabbits is where t is the number of years after the rabbits are introduced, about how long does it take for the rabbit population to reach 130? 9 years 7 years 11 years 10 years The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equation where t is the number of years after 1980. What is the limiting value of the population? 3759 people 23 people 761 people 1, 017 people

Explanation / Answer

a) the data fits the function y=1.3816exp(.3762x) where x is number of years after 1995 and y is number of widgets produced

for 2004 x=9 ;; y =40.8147(41 round figure)

b)30000=6000*(1+r)^n where r is interest rate

5=(1.05)^n

n=33.2 years

c)given S(x)= 5000-11000*exp(-x/8)

for S=1500

x=9.16 months close answer is 9

d) given N=260/(1+75*exp(-.7t))=130

75*exp(-.7t)=1

t=8.898 years (9 years roughly)

e)limiting value of population occurs at t=0

which mean P=3759/4.94=760.93(761 round figure)

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