Question

The population of wolves in a sanctuary has been growing by about 20 wolves a year. In 2012, there were 415 wolves in the sanctuary.
a. Create a linear equation for the number of wolves, P, using the input variable n = number of years since 2012.


b. Create a linear equation for the number of wolves, P, using the input variable t = number of years since 2010.


c. Predict the number of wolves in the sanctuary in 2018. Try using both equations to ensure they agree.
wolves

d. What are the advantages to each way of defining the input variable?

Answer 1

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:

A:

P = Number of wolves

n = number of years since 2012

we know in 2012 there were 415 wolves in the sanctuary, and that the sanctuary has been growing about 20 wolves a year.

P = 20n + 415

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 20 wolves a year, and n is the number of years since 2012. As well as obviously, we add 415 to our equation because there is already 415 wolves in the sanctuary.

B:

P = Number of wolves

t = number of years since 2010

x = unknown variable(number of wolves in 2010)

P = 20t + x

Here we are trying to identify what x is, in 2012 there was 415, each year the number of wolves grew by 20.

P = 20(2) - 415

P = 40 - 415 = 375

We now know there were 375 wolves in 2010

Hence our equation is P = 20t + 375

C:

First let's plug in our first equation

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

P = 535

Our first equation tells us that in 2018 there will be 535 wolves.

Plug in our second equation

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

P = 535

Both our equations agree, and in 2018 there will be 535 wolves.

D:

The advantage of defining the input variable is that it helps simplify the calculation and makes it more intuitive.