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Assume that the current population of a large region is 277 million. It was reported that the population grew 10.9%since it was last measured 10 years previously. Use the model A=A0e^kt

What was the population when it was measured 10 years ago>????

What was the annual rate of growth???

Assuming same rate of growth, how many years from the current year will  the region will have a population of 400 million?________-

Mar 26, 2020

#1
+1956
+2

Imma leave this to CPhill. LOL

Mar 26, 2020
#2
+111321
+2

a)   Since the population grew by 10.9% in the last 10 years......we have that

A0 * ( 1.109)  =  277    divide both sides  by  (1.109)

A0  =   277 / (1.109)   ≈  250

b ) So   to find the annual growth  rate  we  can solve  for  this

277  = 250e ^(k * 10)      divide both sides  by  250

277/250   e ^(10k)       take the Ln of both sides

Ln  (277/250)  = Ln e^(10k)      and we can write

Ln (277/250)  = 10k * Ln e           Ln e   =1

LN (277/250)  / 10   =  k  ≈ .01025   =  annual  growth rate of ≈ 1.025 %

c)   400  = 277 e ^(.01025 * t)        divide both sides by 277

400 / 277  = e^(.01025 * t)       take the Ln again

Ln (400 /277)  = .01025 t     divide  both sides  by   01025

Ln (400/277) / .01025  = t ≈ 35.8   years from the first year =  25.8 years from now

Mar 26, 2020
edited by CPhill  Mar 26, 2020
#3
+23562
+2

1.109 x  = 277

x = 249.77   10 years ago

277 = 249.77 ek(10)

k = .0103458

400 = 249.77 e.0103458t

yields t = 45.51 years    from the time the population was   249.77  (ten years ago)      35.51 years from population of 277 million (presently)

Mar 26, 2020