Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research.
Which insect population is growing at a faster rate?

a The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week.
b The bee hive is growing at a faster rate. It will multiply by 3.8 each week while the ant colony will add 3.8 each week.
c The ant colony is growing at a faster rate. It will add 3.8 each week while the bee hive will subtract 3.8 each week.
d The bee hive is growing at a faster rate. It will add 3.8 each week while the ant colony will divide by 3.8 each week.

The ants have an exponential growth. After each week, the colony multiplies by 3.8. If the first week had 3.8, the 2nd week would have 14.44, 3rd would have 54.9 and so on. On the other hand, the beehive just adds 3.8 after each week. It means that the second week would have 7.6, 3rd week would be 11.4, and so on.

Thus, the answer is letter A.

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AFOKE88 AFOKE88 · Answer 2 · 2022-07-15T12:36:19+02:00

A. The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week.

How to find population growth?

The ants have an exponential growth because the equation is y = 3.8ˣ.

Now after each week, the colony multiplies by 3.8.

First week is; y = 3.8¹ = 3.8

Second week would have; y = 3.8² = 14.44.

Third week would have; y = 3.8³ = 54.9.

However, the second one which is bee hive growth adds 3.8 after each week. This means that;

The second week would have; 2 * 3.8 = 7.6

The 3rd week would have; 3 * 3.6 = 11.4.

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