Question

The number of penguins on an iceberg is
modeled by the equation P(t) = 24(1.231)^t
where t is years since 2010. If
the iceberg has a population of 70 penguins it
will begin to sink and the penguins will have to
find a new home. In
what year are the penguins going to find a new home?

Answer 1

The function of the number of penguins is an exponential function

The penguins are going to find a new home in 2015

How to determine the year

The equation of the function is given as:

$P(t) = 24(1.231)^t$

When there are 70 penguins, the equation becomes

$24(1.231)^t =70$

Divide both sides by 24

$1.231^t =2.917$

Take the logarithm of both sides

$t\log(1.231) =\log(2.917)$

Divide both sides by log(1.231)

$t =5$

The time is 5 years from 2010.

So, we have

Year = 2010 + 5

Year = 2015

Hence, the penguins are going to find a new home in 2015

Read more about exponential functions at:

https://brainly.com/question/11464095