Question

A bucket containing 5 gallons of water begins to evaporate. Each hour the bucket loses 3% of its water. If g is gallons of water after evaporating for t hours, which type of model would best describe the relationship between g and t?

Answer 1

The model that best describes the relationship between g and t is an exponential function

`g(t)=5(0.97^t)`

Explanation:

In this problem we have a exponential function of the form

`g(t)=a(b^t)`

where

g(t) represent the gallons of water after evaporating

t is the number of hours

a is the initial value or y-intercept of the exponential function

b is the base

r is the rate

b=(1+r)

In this problem we have

`a=5\ gal` ---> initial gallons of water into the bucket

`r=-3\%=-3/100=-0.03` ---> is negative because is a decay rate

`b=1-0.03=0.97`

substitute

`g(t)=5(0.97^t)`

therefore

The model that best describes the relationship between g and t is an exponential function