(a) Find the exponential growth or decay model
y = ae^(bt) or y = ae^(−bt)
for the population of each country by letting
t = 10
correspond to 2010. Use the model to predict the population of each country in 2030.

Country 2010 2020
Country A 8.7 7.2
Country B 32.9 37.3
Country C 1360.5 1422.6
Country D 62.3 65.4
Country E 305.7 343.9

Question

(a) Find the exponential growth or decay model 
y = ae^(bt) or y = ae^(−bt)
 for the population of each country by letting 
t = 10
 correspond to 2010. Use the model to predict the population of each country in 2030.

Country	 2010	 2020
Country A	8.7         	7.2
Country B	32.9	          37.3
Country C	1360.5	1422.6
Country D	62.3    	65.4
Country E	305.7	343.9

anonymous · Answer

pls help:(

anonymous · Answer

Do you understand the fundamental difference between the population growth trends in either model?
$$\large y=ae^{bt}\quad\text{vs}\quad y=ae^{-bt}$$

anonymous · Answer

i have no idea how to approach this problem

campbell_st · Answer

ok... so they have given you the model as well as 

A, y and t

so to start you need to find k, the growth constant... 

so for country A you know 
you are given the initial population a = 8.7 , and then 10 years later t = 10 you are given y = 7.2   so the population is in decline.. and k will be negative. 

so to solve for k start with 
 
$$7.2 = 8.7 e^{10k}$$

then dividing both sides by 8.7 you get

$$\frac{7.2}{8.7} = e^{10k}$$

to find k, you need to take the base e log of both sides

$$\ln(\frac{7.2}{8.7} )= 10k$$

then divide both sides of the equation to find k. 

$$k = \frac{\ln(\frac{7.2}{8.7})}{10}$$

then when you have k, substitute it into the model along with a = 8.7 and t = 20 to find the population in 2030. 

hope it helps

anonymous · Answer

yes! can u help with one more question?