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Damm [24]
3 years ago
10

Marta invests $8500 in a new savings account which earns 5.0% annual interest, compounded continuously. What will be the value o

f her investment after 5 years?

Mathematics
1 answer:
Mariulka [41]3 years ago
4 0

Given:

Investment = $8500

Rate of interest = 5.0%

Time = 5 years

Compounded continuously

To find:

The value of investment after 5 years.

Solution:

Rate = 5.0%

        =\frac{5}{100}

Rate = 0.05

Compound interest formula if interest compounded continuously:

A = P e^{rt}

where P is the investment and r is the rate and t is the time.

A = 8500 \times  e^{0.05 \times 5}

A = 8500 \times  e^{0.25}

The value of e^{0.25}=1.284025.

A = 8500 \times  1.284025

A=10914.21

The value of the investment after 5 years is $10914.21.

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Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 8x+4 intersect are the solutions o
Luda [366]
Part 1)
We have two lines:  y = 2-x   and   y = 8x+4
Given two simultaneous equations that are both required to be true.
the solution is the points where the lines cross
Which is where the two equations are equal
Thus the solution that works for both equations is when
2-x = 8x+4
because
where that is true is where the two lines will cross and that is the common point that satisfies both equations.

Part 2) Make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3

see the attached table
The table shows that none of the integers from [-3,3] work because in no case does
<span>2-x = 8x+4
</span>
To find the solution we need to rearrange the equation to the form x=n
2-x =8x+4
8x+x=2-4
9x=-2
x=-2/9

 The only point that satisfies both equations is
where
 x = -2/9
Find y:
   y = 2-x  = 2 - (-2/9) = 2 + 2/9 = 20/9
Verify we get the same in the other equation
y = 8x+4   =  8(-2/9) + 4 = 20/9 
Thus the only actual solution, being the point where the lines cross,
 is the point (-2/9, 20/9)------> (-0.22,2.22)

Part 3) how can you solve the equation 2−x = 8x+4 graphically?
<span>The point on the graph where the lines cross is the solution to the system of equations
</span>
using a graph tool
see the attached figure

the solution is the point (-0.22,2.22)

4 0
3 years ago
And animals weight change from 12 pounds to 16 pounds what was the percent increase to the nearest whole number
amm1812
That's a 33% increase.

I calculated this using the formula:

\frac{|n-o|}{o} * 100

Where n = the new value (16 in your question), o = the old value (12 in your question) and the result is outputted as a percent increase.  You can check that this is correct by finding 33% of 12, adding the result to 12, and checking that the result equals your "new" number.  

Note that 33% is only an approximation as your question requires a number rounded to the nearest whole.


5 0
3 years ago
If 9975 kg of wheat is packed in x bags, how much wheat will each bag contai
vlada-n [284]

Answer:

how many bags because you just said bags?

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2 years ago
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Answer:

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2 years ago
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