Steve collects oysters for a living and sells them to restaurants. while catching oysters, steve keeps track of the total weight of his bag of oysters. a graph of the total weight, in ounces, of steve's bag of oysters, y, with respect to the amount of time that he spends looking for them in minutes, x, is shown below.

what is the average rate of change over the interval [2, 10]?

20 ounces of oysters per minute
8 ounces of oysters per minute
2 ounces of oysters per minute
10 ounces of oysters per minute
5 ounces of oysters per minute

5 ounces of oysters per minute

Step-by-step explanation:

We are given a graph of the total weight, in ounces, of Steve's bag of oysters, y, with respect to the amount of time that he spends looking for them in minutes, x,

Now we are supposed to find the average rate of change over the interval [2, 10]

Formula of Average rate :

Now At x = 2 , f(2)= y = 20

At x=10  , f(10)= y = 60

Substitute the values in the formula

Average rate :

Average rate :

Average rate :

Average rate :

Thus he average rate of change over the interval [2, 10]  is 5 ounces of oysters per minute

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