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# Math problems

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I appreciate any help I can get!

The size of a certain population of wild horses varies because of certain ecological pressures. In 1999, the number of horses was 100. In 2002, the population was down to 60, but in 2005, the population was back up to 100.
a) Assume that 100 was the maximum number of horses and 60 was the minimum. Write an equation that models the size of the population of horses, in terms of what year it is, starting with 1999.
b) What is the equation of the axis of this equation, and what does it represent?
c) How many horses were there in 2000?
d) How many horses should there be in 2015?

May 19, 2017

#1
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Here's a possibility using the graph  of  y  = 20sin(πx / 3  +  π / 2)  + 80

Look at the graph, here :  https://www.desmos.com/calculator/derjhfgw9m

At  x  =  0   (representing year 1999)  we have 100 horses

At x  =  3  ( representing year 2002 )  we have 60 horses

And again, at x = 6 (representing year 2005 )  we're back up to 100 horses

Sorry, I don't understand what "b"  is asking for

c)  In 2000  ( x = 1)  there were 90 horses

d) In 2015  ( x = 16) there were 70  horses

May 19, 2017
#2
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OK.....I believe that the equation of the two axis  are   x  = pi/ 2 and  y  = 80

They represent the horizontal and vertical shifts of the graph

May 19, 2017
edited by CPhill  May 19, 2017