SAT Math X

Algebra Level 1

The estimated population of rabbits in a certain forest is given by the function $P(t)=at+120$ where $t$ is an integer which represents the number of years after the rabbit population was first counted, $0\le t \le 10$ , and $a$ is a constant. If there were $192$ rabbits $3$ ears after the population was first counted, how many rabbits will there be $7$ years after the population was first counted?

288 316 262 384

3 solutions

Mohammad Saleem
Mar 13, 2015

Given: 192 = a3 + 120

a = 24

x = 24*7 + 120

288

Krishna Garg
Aug 29, 2014

from given corelation we need to find value of constant a. with 3 yrs equation is 3a + 120 = 192 ,so valua of a is 24. substituting this value for 7 yrs we get 7 x 24 + 120 = 288 Ans K.K.GARg,India

John M.
Aug 28, 2014

We can't figure out how many rabbits there were after $7$ years until we know the constant $a$ . To find it, let's use one of the data points that we're given.

We know that after (3) years ( $t=3$ ) there were $192$ rabbits ( $P(t)=192$ ). Plug both of those into the equation and we get $192=a(3)+120$ , which we can solve to find $a=24$ . Now plug that into our original equation, and we have $P(t)=24t+120$ .

To find out how many rabbits there were after $7$ years, plug in $t=7$ : $P(t)=24(7)+120=\boxed{288}$ .

Solution credit: The Princeton Review

SAT Math X

3 solutions

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