logb(x) = y is equivalent to b^y =x
y = 2
b = 5
x = 25
Substitute the values to get 5^2 = 25
ANSWER
2(s+175)
EXPLANATION
The total amount of garbage thrown away at the school each day is the amount of garbage thrown away by the students plus the amount of garbage thrown away by non-students.
total = lb students + lb non-students
lb students is 2s as each student throws away two pounds a day.
lb non-students is 350. Therefore, the total amount of pounds of garbage thrown away each day is
total = 2s + 350
We can factor out a 2 from this expression as each term is divisible by 2 and that is the greatest common factor. We end up with
total = 2(s+175)
The answers will be:
- (4, 5)
- remain constant and increase
- g(x) exceeds the value of f(x)
<h3>What is Slope and curve?</h3>
a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).
b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).
c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:
f(8) = 4·8 +3 = 35
g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35
g(8) > f(8)
d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).
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