S MATH echang125 \#14 Usten populations of two cities after \( t \) years can be modeled by \( -300 t+150,000 \) and \( 500 t+200,000 \). What difference in the populations of the cities when \( t=6 \) ? people Previous 5 6 7 8 9 10 11 12 13 14 Overview
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City 1: \( -300t + 150,000 \) City 2: \( 500t + 200,000 \) Show more…
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These exercises use the population growth model. Population of a City The population of a certain city was $112,000$ in $2014,$ and the observed doubling time for the population is 18 years. (a) Find an exponential model $n(t)=n_{0} 2^{f / a}$ for the population $t$ years after 2014 . (b) Find an exponential model $n(t)=n_{0} e^{r t}$ for the population $t$ years after 2014 . (c) Sketch a graph of the population at time $t .$ (d) Estimate how long it takes the population to reach $500,000 .$
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These exercises use the population growth model. The population of a certain city was 112,000 in 2014 , and the observed doubling time for the population is 18 years. a. Find an exponential model $n(t)=n_{0} 2^{t / a}$ for the population $t$ years after 2014 b. Find an exponential model $n(t)=n_{0} e^{r t}$ for the population $t$ years after 2014 c. Sketch a graph of the population at time $t$ d. Estimate how long it takes the population to reach 500,000 .
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In a particular county, the population of the two largest cities can be modeled by f(x) = 200x +25 and g(x) = 175x -15, where x is the number of years since 2010 and the population is in the thousands. a) what is the population of the two cities combined after any number of years? b) what is the difference in populations of the two cities?
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