Roscoe rides his bike at least 10 miles but not more than 30 miles. he rides at an average rate of 10.5 miles per hour. the amount of time it takes for roscoe to ride his bike  m  miles is represented by a function.   t(m)= m 10.5 what is the practical domain of the function? all integers from 0 to 50, inclusive all integers from 10 to 50, inclusive all real numbers all multiples of 20 between 0 and 1000, inclusive explain how you got your answer too, you!

Actually, the domain is the possible set of input values of a function that will make the function fit the specific criteria. In this case, the input value is m, where m is the number of miles that is travelled. The criteria is to travel at least 10 miles but not more than 30 miles, therefore the domain should be:

All real numbers from 10 to 30, inclusive

(should be real numbers not integer since any fractional number is included in the domain)

I cannot figure out why the choices are far from the answer.

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

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