Question

A population of insects grows exponentially, as shown in the table. Suppose the increase in population continues at the same rate. What is the insect population at the end of week 11? Round to the nearest whole number.
At the end of the week 0 1 2
Insect population 20 30 45

Answer 1

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,

$y=ab^x$

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)

$\Rightarrow 20=ab^0$

$\Rightarrow a\cdot (1)=20$

$\Rightarrow a=20$

Now the exponential function becomes,

$y=20b^x$

At (1, 30)

$\Rightarrow 30=20b^1$

$\Rightarrow 20b=30$

$\Rightarrow b=\dfrac{30}{20}$

$\Rightarrow b=\dfrac{3}{2}$

Now the equation becomes,

$y=20(\frac{3}{2})^x$

For calculating the number of insects at the end of the 11th week, putting x=11, so

$y=20(\frac{3}{2})^{11}$

$=1729.95 \approx 1730$

Answer 2

The correct answer would be 1730 just took the test and got this correct. :)