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Math·Advanced Math·Nonlinear functions

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A computer program models the population of a certain insect in an environment where the insect has no natural predators. According to the model, the estimated total mass of the population of insects at the end of every 5-week period is 158% greater than the estimated total mass of the population of insects at the end of the previous 5-week period. The estimated total mass of the population of insects at the end of 15 weeks is 627.7 grams.

Which equation best represents this model, where M is the estimated total mass, in grams, of the population of insects at the end of t weeks?

A

$M=538.92(1.58{)}^{\frac{t}{5}}$

B

$M=457.66(2.58{)}^{\frac{t}{5}}$

C

$M=159.14(1.58{)}^{\frac{t}{5}}$

D

$M=36.55(2.58{)}^{\frac{t}{5}}$