+318 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?________-
+128473 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
+36916 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)
