Question

Since the year 2000 I've collected statues of frogs, and now that my family knows this, I get the same number of frogs every year. In 2010 I owned 104 frog statues, and in 2014 I owned 136 frog statues. Let x be the years since 2000, and y be the number of frog statues I own. Find an equation for the number of frog statues Town in a given year, and then use your equation to find the number of statues I had in 2000 when I started my collection, and the number of frog statues I expect to own in 2025.

Answer 1

Our equation model will be of the form.

y= ax +b, let us use known values to get a and b

In 2010, you owned 104 frog statues, here, x = 2010 - 2000 = 10, y=104

so 104 = 10a + b

In 2014, you owned 136 frog statues, here, x = 2014 - 2000 = 14, y = 136

so, 136 = 14a + b.

Lets solve this system of equation simultaneously,

136 = 14a + b ---1

104 = 10a + b ---2

Subtract equation 2 from 1, we have

32 = 4a, a = 32/4 = 8

Plug 8 into equation 1

136 = 14(8) +b , b = 136 - 112 = 24

So, our equation is ,

y = 8x + 24

1. in 2000, x = 0, we have y = 8(0) + 24 = 24 frog statues, meaning that you started your collection with 24 frog statues.

2. in 2025, x = 25, thus y = 8(25) +24 = 224 frog statues you expect to own.