Answer:
A: P = 20n +415
B: P = 20t + 375
C: Both equations agree, and in 2018 there will be about 535 wolves
D: The advantage of defining the input variable is that it helps simplify the calculation and makes it more intuitive.
Step-by-step explanation:
<h3>A:</h3>
P = <u>Number of wolves</u>
n = <u>number of years since 2012</u>
<em>we know </em><em>in 2012</em><em> there were </em><u><em>415 wolves in the sanctuary</em></u><em>, and that the </em><em>sanctuary </em><em>has been </em><em>growing about </em><u><em>20</em></u><u><em> wolves </em></u><u><em>a year.</em></u>
<u><em></em></u>
<h3>P = 20n + 415</h3>
we know this is correct because we are trying to create an equation that represents the number of wolves(p) throughout the years(n), so we are trying to figure out what P equals. We know that the sanctuary grows about <u>20</u> wolves a year, and n is the number of years since 2012. As well as obviously,<u> we add 415 to our equation because there is </u><u>already 415 wolves in the sanctuary.</u>
<h3>B:</h3>
P = <u>Number of wolves</u>
t = <u>number of years since 2010</u>
x = <u>unknown variable(number of wolves in 2010)</u>
<h3>P = 20t + x</h3>
Here we are trying to identify what x is,<u> in 2012 there was 415, each year the number of wolves grew by 20.</u>
<h3>P = 20(2) - 415</h3>
P = 40 - 415 = 375
<u>We now know there were 375 wolves in 2010</u>
<h3>
Hence our equation is P = 20t + 375</h3>
<h3>
C:</h3><h3>First let's plug in our first equation</h3>
P = 20n + 415
(To find n all we do is subtract 2018 and 2012, which equals 6.)
P = 20(6) + 415
(Solve)
P = 120 + 415
<h3>
P = 535</h3>
<em>Our first equation tells us that in 2018 there will be 535 wolves.</em>
<em></em>
<h3>
Plug in our second equation</h3>
P = 20t + 375
(To find t all we do the same thing we did last time except now we subtract 2018 from 2010, which equals 8)
P = 20(8) + 375
P = 160 + 375
<h3>P = 535</h3>
<h2>Both our equations agree, and in 2018 there will be 535 wolves.</h2>
<h3>D:
</h3>
The advantage of defining the input variable is that it helps simplify the calculation and makes it more intuitive.
