Answer:
13.2 years
Step-by-step explanation:
The decay rate is 15%, so the decay factor is 1 - 15% = 0.85. Then the exponential equation for the value is ...
v(t) = 85000·0.85^t
We can set v(t) = 10,000 and solve for t:
10000 = 85000·0.85^t
10000/85000 = 0.85^t . . . . divide by 85000
log(2/17) = t·log(0.85) . . . . . .reduce fraction, take logs
t = log(2/17)/log(0.85) ≈ 13.2
It will take about 13.2 years for the value to fall below $10,000.
_____
Such a question is nicely answered by a graphing calculator.
Answer:
B yes, because every x value corresponds to exactly one y value
Step-by-step explanation:
A function means that each input goes to a different output
Each input goes to only 1 y value
Answer:
D. 108 liters
Step-by-step explanation:
Given that the leak is ;
5 drops = 5 minutes
?= 4 weeks
Find number of hours in 4 weeks
1 week=7days
4 weeks=?--------------cross multiply
4×7=28 days
1 day=24 hours
28 days=?--------------cross multiply
28×24=672 hours
Hour= 60 minutes
672 hours=?
672×60=40320 minutes
Finding the leakage in 4 weeks
80 drops= 5 minutes
?=40320 minutes------------cross multiplication
(40320×80)÷5 =645120 drops
Finding the liters of water wasted in 4 weeks
60 drops of water= 10 milliliters
645120 drops of water=?-------------cross multiply
(645120×10)÷60 =107520 milliliters
But you know
1 milliliter=0.001 liters
107520 milliliters=?-----------cross multiply
107520×0.001
=107.52 liters
=108 liters
Answer: I would say that x = 10 degrees
Step-by-step explanation:
The angle has a square, meaning it is a right angle. Right angles are 90 degrees, and you're given 80 degrees + x.
90 - 80 = 10
Hope this helps!
Answer:
Convergent
Step-by-step explanation:
This is an alternating series where bn = 2n / eⁿ. Apply the alternating series test:
lim(n→∞) bn
= lim(n→∞) (2n / eⁿ)
Use L'hopital's rule:
= lim(n→∞) (2 / eⁿ)
= 0
For n ≥ 1, the series is decreasing. 2(n+1) / eⁿ⁺¹ < 2n / eⁿ.
Therefore, the series converges.
