Answer-
The insect population at the end of week 11 is 1730.
Solution-
A population of insects grows exponentially.
The general form of exponential function is,
[tex]y=ab^x[/tex]
Where,
a, b are constants.
Putting the data given in the table, in the the equation in order to get the values of a, b
At (0, 20)
[tex]\Rightarrow 20=ab^0[/tex]
[tex]\Rightarrow a\cdot (1)=20[/tex]
[tex]\Rightarrow a=20[/tex]
Now the exponential function becomes,
[tex]y=20b^x[/tex]
At (1, 30)
[tex]\Rightarrow 30=20b^1[/tex]
[tex]\Rightarrow 20b=30[/tex]
[tex]\Rightarrow b=\dfrac{30}{20}[/tex]
[tex]\Rightarrow b=\dfrac{3}{2}[/tex]
Now the equation becomes,
[tex]y=20(\frac{3}{2})^x[/tex]
For calculating the number of insects at the end of the 11th week, putting x=11, so
[tex]y=20(\frac{3}{2})^{11}[/tex]
[tex]=1729.95 \approx 1730[/tex]
The correct answer would be 1730 just took the test and got this correct. :)
