The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive. which function best models the data?

The exponential function best models the data for the given table.

Step-by-step explanation:

Given : The table showing the estimated number of bees, y, in a hive x days after a pesticide is released near the hive.

We have to find which function best models the data for the given table.

Consider the given data in the table.

We first plot the data using Expo- regression calculator (as shown in attachment)

Since, The the estimate number of bees deceases with increasing number of days ,thus the data represents an exponential decay over time.

Thus, The exponential function best models the data for the given table.

And the equation of model is given as

Where y represents the  estimate number of bees

and x represents the number of days.

the answer to the expression is 83

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!