Mathematics, 27.07.2019 21:00 leobaut6145

The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table. the function is quadratic, rainfall(in.) .population (millions.) 0. 0 1. 9 3. 21 4. 24 5. 25 6. 24 the x-intercept represents that after in. of rain there are mosquities. ( i cant seem to wrap my head around this, if you can just me start somehwere i'd really appriciate it. also i noticed the pattern in mosquitoes.)

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Answer from: Senica

The x-intercept represents that after 10 in. of rain there are mosquitoes.

The x-intercept represents that after 0 in. of rain there are no mosquitoes.

Step-by-step explanation:

We are given a table that represents the population of mosquitoes in a certain area as a function of inches of rainfall :

RAINFALL(in.) POPULATION (millions.)

0 0

1 9

3 21

4 24

5 25

6 24

We will first find the function P(t) which denotes the number of mosquitoes after t inches of rainfall.

As the function is quadratic.

Hence , let:

P(t)=at^2+bt+c

At t=0 we have, P(t)=0

c=0

at t=1 we have: P(t)=9

i.e.

a+b=9-----(1)

Also at t=2 we have: P(t)=21

i.e.

9a+3b=21-------(2)

On solving equation (1) and (2) we get:

a= -1 and b=10

Hence,

P(t)=-t^2+10t

We know that the x-intercept of a graph is a point where the y-value is zero.

i.e. it is the inches of rainfall when the population of mosquitoes is zero i.e. there are no mosquitoes.

i.e. we have to find t such that:

P(t)=0

i.e.

$-t^2+10t=0\\\\i.e.\\\\t(10-t)=0\\\\i.e.\\\\ t=0\ or\ t=10$

Hence, we have got two x-intercept.

one at t=0 and the other at t=10.

The x-intercept represents that after 10 in. of rain there are no mosquitoes.

The x-intercept represents that after 0 in. of rain there are no mosquitoes.

Answer from: Tdhaynes7759

The x-intercept represents that after 10 in. of rain there are mosquitoes.

Step-by-step explanation:

The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table.

The function is quadratic, P(x)=ax^2+bx+c

where, P represents number of mosquitoes in millions. x represents rainfall in inches.

Table :

x : 0 1 3 4 5 6

P : 0 9 21 24 25 24

Using three point to make system of equation and solve for coefficients a, b and c

Put (0,0) and we get c=0

Put (1,9) and we get a+b+c=9

Put (3,21) and we get 9a+3b+c=21

Solve for a, b and c

a=-1

b=10

c=0

P(x)=-x^2+10x

Now, we will find x-intercept of the function. Put P(x)=0 and solve for x

-x^2+10x=0

x=0,10

The x-intercepts represent number of mosquitoes after 10 in of rain fall.

Answer from: Quest

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Answer from: Quest

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