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Answer:
The x-intercept represents that after 10 in. of rain there are mosquitoes.
Or
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:
At t=0 we have, P(t)=0
at t=1 we have: P(t)=9
i.e.
Also at t=2 we have: P(t)=21
i.e.
On solving equation (1) and (2) we get:
a= -1 and b=10
Hence,
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.
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.
Or
The x-intercept represents that after 0 in. of rain there are no mosquitoes.