Since $t$ represents the number of years passed since 2005, in 2005 we have $t=0$ , and in 2015 we have $t=10$ . Let $P_J(y),P_D(y)$ represent the profits of Jones and Davis, respectively, at year y.

We have

$P_J(2005) = 10(0.99)^0 = 10,\quad P_J(2015) = 10(0.99)^{10}\approx 9$

$P_D(2005) = 8(1.01)^0 = 8,\quad P_D(2015) = 8(1.01)^{10}\approx 9$

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 $0.99^t$ goes to zero as t grows.

On the other hand, Davis starts with a smaller value, but $1.01^t$ 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

$8\cdot 1.01^t = 10\cdot 0.99^t \iff 0.8 = \left(\dfrac{0.99}{1.01}\right)^t \iff t\approx 11$

So, after 11 years, Davis will overcome Jones.

3 0

2 years ago

To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before ad

Kryger [21]

Answer:

The first equation should be multiplied by 9 and the second equation by −4

Step-by-step explanation:

Given the simultaneous equation

First Equation: 5x − 4y = 28

Second equation: 3x - 9y = 30

In order to eliminate y, we must make the coefficient of x in both expression to be equal.

To do that the first equation should be multiplied by 9 (negative value of the coefficient of y in equation 2)and the second equation by -4( (coefficient of y in equation 1)

7 0

2 years ago

I need help with this asap! i will give brainliest!!

oee [108]

Answer:

Step-by-step explanation:

Angle on a straight line = 180

106 + ∠st = 180

∠st = 180 - 106 = 74

x = ∠st + 23

= 74 + 23

= 97

4 0

2 years ago

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