For any exponential function, f(x) = abx, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.
Overall, the steps for algebraically finding the range of a function are:
Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
Find the domain of g(y), and this will be the range of f(x).
If you can't seem to solve for x, then try graphing the function to find the range.
Answer
A. -30 points
B. 60 points
Step-by-step explanation:
20 points for correct answer and 10 points deducted for wrong answer
Each deduction is -10 while each correct answer gives + 20
4 questions correctly and 11 incorrectly
= 4(20) + 11(-10)
= 80-110 = -30 points
Second round
7 correct, 8 incorrect
= 7(20) - 8(10)
= 140-80 = 60 points
The rigth equation to anticipate the profit after t years is p(t) = 10,000 (1.075)^t
So, given that both store A and store B follow the same equations but t is different for them, you can right:
Store A: pA (t) 10,000 (1.075)^t
Store B: pB(t'): 10,000 (1.075)^t'
=> pA(t) / pB(t') = 1.075^t / 1.075^t'
=> pA(t) / pB(t') = 1.075 ^ (t - t')
And t - t' = 0.5 years
=> pA(t) / pB(t') = 1.075 ^ (0.5) = 1.0368
or pB(t') / pA(t) = 1.075^(-0.5) = 0.964
=> pB(t') ≈ 0.96 * pA(t)
Which means that the profit of the store B is about 96% the profit of store A at any time after both stores have opened.
Arithmetic sequence: must have a constant common difference.
3/20-1/10=(3-2)/20=1/20
5/30-3/20=(10-9)/60=1/60
Difference is not constant, so no.
Geometric sequence: must have a common ratio
30/20 / (1/10) = 15
5/30 / (3/20) = 100/90 = 10/9
ratio is not constant, so no.
The answer is (c) neither geometric nor arithmetic
