find a function

Question

the populaion of scorpions starts at 25 in your house. they increase at a rate of 58% annually. Write a function showing the growth rate and then caculate the rate after 3 years

Answer 1

x = 0 then y = 25

x = 1 then y =(1.58)*25  This would be the 58% increase

x = 2 then y = (1.58)²*25 this would be the growth over two years

 

another way to right this is to realize that each year (each value of x) we are mutliplying by (1.58) raised to power

 

when x = 0 we raise (1.58) to the zero power

when x = 1 we raise (1.58) to the first power

when x = 2 we raise (1.58) to the second power

 

or in each case we raise (1.58) to the x power

 

so our equation becomes

 

y = (1.58)^x* 25  (and we can use this to solve for any value of x)