Question

The graph shows the populations (in millions) of Bulgaria and Tajikistan from 2006 through 2013 using exponential models. Tajikistan Population (in millions) Bulgaria 6 7 12 13 8 9 10 11 Year (6 4 2006) (a) Determine whether the population of Tajikistan is modeled by exponential growth or exponential decay. Explain your reasoning. • The population of Tajikistan is decreasing; therefore, it must be an exponential decay model. The population of Tajikistan is increasing; therefore, it must be an exponential growth model. The population of Tajikistan is decreasing; therefore, it must be an exponential growth model. The population of Tajikistan is increasing; therefore, it must be an exponential decay model. Determine whether the population of Bulgaria is modeled by exponential growth or exponential decay. Explain your reasoning. The population of Bulgaria is decreasing; therefore, it must be an exponential decay model. The population of Bulgaria is increasing; therefore, it must be an exponential growth model. The population of Bulgaria is decreasing; therefore, it must be an exponential growth model. The population of Bulgaria is increasing; therefore, it must be an exponential decay model. (b) Estimate the year when the two countries had the same population. What was this population? The two countries appear to have the same population of about million in the year

Answer 1

a) from graph the population of Tajikistan is increasing as the time in years are increasing so this can be modeled as exponential growth since there is growth rate k is increasing

Exponential decay ok goowth: If y(t) is the population after 't years, then this can be modeled by differential egr (bes there will be change in y(t) by years), then kis the growth rate dy = ky Rate of change of population Rate of change of population as' k" Increases as 'k' decreases Growth rate k increases population increases as population decreases y = cekt (solution ) g=cent (solution) Exponential Growth Exponential Decay Cast increases, y Increased cast increases, y decreases

So option 2 IS CORRECT :THE POPULATION OF TAJIKISTAN IS INCREASING, THEREFORE IT MUST BE EXPONENTIAL GROWTH MODEL

2)from graph the population of Bulgaria is decreasing as time increasing this can be modeled as exponential decay because there is growth rate decreasing nothing but decay

OPTION 1 IS CORRECT

b) the both population lines are intersecting at one place

At this intersection the population are same for two countries at some time t

Population is 7.25 millions and time t= 8.1 nearly

The two countries appear to have the same population of about 7.25 million in the year 2008. (2008.1 )

Since 6 represents 2006 and 8 for 2008