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JulijaS [17]
11 months ago
11

a lump sum of $2000 is invested at 4.2% compounded continuously. (a) write the function for the model that gives the future valu

e of the investment in dollars after t years. f(t)
Mathematics
1 answer:
katrin2010 [14]11 months ago
4 0

The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t

Give, a lump sum of $2000 is invested at 4.2% compounded continuously.

Hence we have:

P = $2000

rate of interest = 4.2%

years = t

we know that A = Pe^rt

Substitute the above values in the formula.

Amount = f(t)

f(t) = 2000.e⁰·°⁴²t

hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t

Therefore we get the required function.

Learn more about Compound Interest here:

brainly.com/question/2455673

#SPJ4

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A plane flying horizontally at an altitude of 1 mile and a speed of 570 mi/h passes directly over a radar station. Find the rate
valina [46]

The rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

We assume the station to be at point A.

The plane when directly over the station, takes point C.

As it is flying horizontally continuously at an altitude of 1 mile, AC = b = 1 mile.

The plane flies continuously, and when it is at a distance of 3 miles from the station, it is at point B.

The distance between the plane and the station of 3 miles can be shown as AB = c = 3 miles.

The movement of the plane from C to B can be shown as BC = a.

Now, from the given case, we get a right triangle ABC.

By Pythagoras' Theorem,

a² + b² = c² ... (i).

or, a² + 1² = 3²,

or, a² = 9 - 1 = 8,

or, a = 2√2 miles.

We are told that the plane is moving at a speed of 570 miles/hour.

This can be shown as, da/dt = 570 miles/hour.

As the plane is moving horizontally, the vertical distance between the plane and the station doesn't change, that is, db/dt = 0.

In the question, we are asked to find the rate at which the distance from the plane to the station is increasing, that is, we are asked to find dc/dt.

Differentiating (i), with respect to time t, we get:

2a(da/dt) + 2b(db/dt) = 2c(dc/dt).

Substituting values of a = 2√2 miles, b = 1 mile, c = 3 miles, da/dt = 570 miles/hour, and db/dt = 0, we get:

2(2√2)(570) + 2(1)(0) = 2(3)(dc/dt),

or, 2280√2 + 0 = 6(dc/dt),

or, dc/dt = 380√2 miles/hour = 537.40 miles/hour ≈ 537 miles/hour.

Thus, the rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

Learn more about the Pythagoras Theorem and Differentiation at

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2 years ago
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leonid [27]
The best buy is the in. I really hope this helped
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3 years ago
Determine if the lines are parallel, perpendicular, or neither 10x+5y=-5 and y=-2x+6
Ksenya-84 [330]
If they are parallel they will have the same slope , m

So in y = mx + c, if there are two equations which both have the same m value they will be parallel.
If the lines are perpendicular they'll have slopes like this: 1/2 to -2/1 - where they flip and a negative gets added.

In the equations: 10x + 5y = -5 , and y = -2x + 6
We can rearrange 10x + 5y = -5 to be in the form y = mx + c
10x + 5y = -5
5y = -5 - 10x
y = -1 - 2x
y = -2x - 1

Since y = -2x - 1 and y = -2x + 6 both have the same slope of -2 they are parallel!

7 0
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Finish writing the equation of the line y= -3/2x+?, given the points (6, -5) and (-2, 7).
anastassius [24]

Answer:

y=-3/2x+4

Step-by-step explanation:

In order to solve this you need to graph the points and then draw a line threw them. The place where the line crosses through the y-intercept is the value for b in y=mx+b.

6 0
2 years ago
What is the value of f? −1/8f−3/4−1/4f=11?
cluponka [151]
I hope this helps you

8 0
2 years ago
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