Question

The turtle population on an island is declining at a rate of 1.4% per year. The population was 3800 in the year 2009.

Which answer is the best prediction of the population in the year 2014?

A. 3541

B. 3592

C. 3643

D. 3747

Answer 1

D?

Answer 2

Hm... so lets think about this.
\[A=A _{0}b^t\]
Where Ao = initial
b= decay factor (1-percent of decay)
t=years.

Answer 3

@Yuii
if Ao=3800 & the percent of decay is 0.014 (1.4%)
... What is the equation?

Answer 4

5320?

Answer 5

hmm..

\[A=3800(1-0.014)^x\]
This right? Let x= years since 2009 & A= turtle population?

Answer 6

I did
\[3800 * 1.4%\]

Answer 7

I think that's where I messed up.

Answer 8

Yep...
so that is the percent of decay... when you plug it in to the function convert it to decimals.. the DECAY FACTOR is 1-percent of decay (in decimals)

Answer 9

\[3800 * 0.986^x\]

I'm doing this wrong, aren't I?

Answer 10

Nope! Looks all good... so they're asking about the turtle population in 2014... aka 5 years after 2009 (initial)

What is the population?

Answer 11

In 2009 the population was 3800.

Is that what you're asking or for 2014?

Answer 12

yep... which is 5 years after 2009.

so
\[A=3800(.986)^5\]-->

=??

Answer 13

A = 3541.34446...

So, A.

Answer 14

Yep :D

Answer 15

Thank you for your help.

Answer 16

Anytime (: