Sage belongs to a bird-watching club. Every two days, she goes out and counts the number of Black-hooded Parakeets she sees. The sightings can be approximated by the equation y = 1/2x + 3. What is the approximate rate of change for the number of parakeets seen?

3

1/2

-1/2

7/2

The rate of change for the number of parakeets seen is 1/2

Step-by-step explanation:

The sightings can be approximated by the equation:

y = (1/2)*x + 3

Which represents a line. Any line can be writen by an equation in the following form:

y = m*x + b

Where m is the slope of the lane or it's rate of change and b is the value for "y" when "x" equals zero. Applying this knowledge to the equation of the bird sightings we can se that the sightings grows 1/2 for every one unit that x grows, therefore the rate of change is 1/2.

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 5

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places