Since
represents the number of years passed since 2005, in 2005 we have
, and in 2015 we have
. Let
represent the profits of Jones and Davis, respectively, at year y.
We have
![P_J(2005) = 10(0.99)^0 = 10,\quad P_J(2015) = 10(0.99)^{10}\approx 9](https://tex.z-dn.net/?f=P_J%282005%29%20%3D%2010%280.99%29%5E0%20%3D%2010%2C%5Cquad%20P_J%282015%29%20%3D%2010%280.99%29%5E%7B10%7D%5Capprox%209)
![P_D(2005) = 8(1.01)^0 = 8,\quad P_D(2015) = 8(1.01)^{10}\approx 9](https://tex.z-dn.net/?f=P_D%282005%29%20%3D%208%281.01%29%5E0%20%3D%208%2C%5Cquad%20P_D%282015%29%20%3D%208%281.01%29%5E%7B10%7D%5Capprox%209)
Choosing the best company somehow depends on how much time you can wait: Jones start with a higher value (10 vs 8), but it has a descending trend, because the multiplicative factor
goes to zero as t grows.
On the other hand, Davis starts with a smaller value, but
tends to infinity as t grows.
So, if you need an immediate result, the most valuable company is Jones, otherwise you're certain can Davis will eventually become bigger.
More precisely, we have
![8\cdot 1.01^t = 10\cdot 0.99^t \iff 0.8 = \left(\dfrac{0.99}{1.01}\right)^t \iff t\approx 11](https://tex.z-dn.net/?f=%208%5Ccdot%201.01%5Et%20%3D%2010%5Ccdot%200.99%5Et%20%5Ciff%200.8%20%3D%20%5Cleft%28%5Cdfrac%7B0.99%7D%7B1.01%7D%5Cright%29%5Et%20%5Ciff%20t%5Capprox%2011%20)
So, after 11 years, Davis will overcome Jones.
Answer:
a) bijective
b) neither surjective or injective
c) injective
Step-by-step explanation:
Since we are looking from real numbers to real numbers, we want the following things
1) We want every real number y to get it. (surjective)
2) We want every y that gets hit to be hit only once. (injective).
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If we have both things then the function is bijective.
a) f(x)=5x+4 this is a line with a positive slope.
That means it is increasing left to right. Every increasing or even decreasing line is going to hit every real number y. This is a bijection.
b) g(x)=2x^2-2 is a parabola. Parabola functions always have y's that get hit more than once and not all y's get hit because the parabola is either open up or down starting from the vertex. This function is neither injective or surjective.
c) h(x)=1+(2/x) x is not 0.
1+(2/x) is never 1 because 2/x is never 0 for any x. This means the real number y=1 will never be hit and is therefore not surjective. This function is injective because every 1 that is hit is only hit once. If you want use the horizontal line test to see this.
Answer:
Step-by-step explanation:
29,484
4, Does not round
the second 4, rounds to 5 because of the 8,
then The 9 would round and be 30
if its a decimal then it would be 30.0
if not then i think it would be 30,500 or 29,500 if we were to stop at the 9 and not round it
Answer:
The cost of 12 gallons of gas and a quart of oil is 14·x - 30
Step-by-step explanation:
When adding variables, the coefficient of the variables are added followed by multiplication of the sum of the coefficients with variable as follows;
The cost of 12 gallons of gas = 12·x
The cost of a quart of oil is represented by 2·x - 30
Therefore, the cost of 12 gallons of gas and a quart of oil can be represented as follows;
12 gallons of gas and a quart of oil = 12·x + 2·x - 30
Which gives;
The cost of 12 gallons of gas and a quart of oil = 14·x - 30.