A population of insects grows exponentially, as shown in the table. Suppose the increase in population continues at the same rate.
from the given table
when x=0 , y=20
when x= 1 , y = 30
We use this information to find exponential growth equation
General form of exponential growth is
[tex]y=a(b)^x[/tex]
WE plug in the given values and find out value of a and b
when x=0 , y=20
[tex]20=a(b)^0[/tex]
20 = a
Now we find out b
when x= 1 , y = 30
[tex]30=20(b)^1[/tex]
divide both sides by 20
[tex]\frac{3}{2} = b[/tex]
So exponential function becomes
[tex]y=20(\frac{3}{2})^x[/tex]
Now we find the insect population at the end of week 11
We plug in 11 for x
[tex]y=20(\frac{3}{2})^x[/tex]
[tex]y=20(\frac{3}{2})^11= 1729.951171875[/tex]
Round the answer to nearest whole number
1730 is the insect population at the end of week 11
