Suppose that $20,000 is invested in an account for which interest is compounding continuously at 3.14%. What is the value after 5 years? After 10 years? (Round your answers to two decimal places.) After how many years will the original investment be doubled? (Round your answer to two decimal places.)

value after 5 years = $23,399.91

after 10 years = $27,377.79

Time it takes for the amount to double = 22.07 years

Step-by-step explanation:

For amounts that are compounded continuously, it means that the interest rate is is added to the investment amount at an infinite number of time, and the formula is given as:

A = P , where:

A = Future value

P = present value

e = constant ≈ 2.7183

r = interest rate in decimal form

t = years

Now for value after 5 years;

A = ???

P = $20,000

r = 3.14% = 0.0314

t =  5 years

∴ A = P

= 20,000

= 20,000 × = 20,000 × 1.169995 = $23,399.91 ( to 2 decimal places)

(Note that the function '' can be punched directly from the calculator)

value after 10 years;

A = ???

P = $20,000

r = 3.14% = 0.0314

t =  10 years

∴ A = P

= 20,000 ×

= 20,000 × = $27,377.79 ( to 2 decimal places)

Time it will take to double the original investment;

A = P

where;

A = 40,000

P = 20,000

r = 0.0314

t =???

40,000 = 20,000 ×

(divide both sides by 20,000)

2 =

Next take the natural logarithm of both sides

㏑(2) = ㏑      (㏑ = 1; and the exponent can be brought down )

= 0.6931 = 0.0314 × t × 1

∴ t = = 22.07 years ( to 2 decimal places)

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!