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3. in australia wheat grain exports are often affected by little...

# Question: in australia wheat grain exports are often affected by little...

###### Question details

In Australia, wheat grain exports are often affected by little insects, it has been estimated that between one quarter and one third of the world grain crop is lost each year during storage and transportation. Even with the strictest safety precautions and protocols, these insects are not completely eliminated. At the start of the voyage, 40 ants remained among the wheat grains in the cargo hold of the ship. One week into the voyage, there were approximately 310 ants. The model used to estimate the number of ants, N, is N(t) = 400/1+9e(to the power of kt)

a) a) although the question says there are 40 ants on the ship at the start of the trip, the exporters wanted independent algebraic proof using the proposed model of N(t)=400/1+9e(to the power of kt) show how the captain used the model to prove there were 40 ants initially

N(0) 400/10 = 40 ants

b) rearrange the model , without substitution of values , to K=

K= In(1/9(400/n(t) -1 )) / 1

c) Now , find the value of k correct to 2 decimal places using all the information from the question