Question

During warm weather, colonies of tiny green algae can grow rapidly in lakes and oceans,forming algal blooms. An algal bloom on Glass Lake doubles in area every week. The bloomcurrently covers an area of 3 square meters.Let t represent the length of time, in weeks, until the bloom covers an area of at least76 square meters. Which inequality can you use to find t?

Answer 1

top left:

`3(2)^t\ge76`

Step-by-step explanation:

The algae area doubles every week, meaning after one week its area will be

`3*2`

after two weeks

`3*2*2`

after 3 weeks

`3*2*2*2`

and so on.

After t weeks the area will be

`3(2)^t`

Now, we want this area to be at least 76 square meters (at least means we use ≥ symbol); therefore,

`3(2)^t\ge76`

which is our answer!