word problem calc

Question

Authorities conducted an investigation and found that the chemical Trioxin was illegally dumped into the local swamp. Exactly four days after the assumed time of the​ crime, the amount of Trioxin in the swamp was estimated at about

45.9

​barrels, and exactly seven days after the​ crime, it was estimated at

28.1

barrels.  Assume that no Trioxin was in the swamp before the​ crime, and that Trioxin decays exponentially.

Construct a model that estimates the amount of Trioxin​ (in barrels) remaining in the swamp t days after it was​ dumped, then use that model to answer the following.

​1) According to the​ model, how much Trioxin was initially dumped into the​ swamp?

ROUND TO ONE DECIMAL PLACE.

About

enter your response here

barrels were initially dumped into the swamp.

​2) According to the​ model, at what rate was the amount of Trioxin in the swamp decreasing exactly 4 days after it was​ dumped?  ROUND TO ONE DECIMAL PLACE.

The Trioxin was decreasing at a rate of

enter your response here

barrels per day.

​3) How many days after the crime​ will/did it take for the amount of Trioxin in the swamp to drop to 2​ barrels?  ROUND TO ONE DECIMAL PLACE.

It took or will take about

enter your response here

days.

Answer 1

28.1 = 45.9e^3k

ln 28.1 = 3k ln 45.9

Solve for k

A(t) = a₀e^kt, using value of k from above.

Can you complete the rest?