8.
if a principal of $2500 was invested at a rate of 5% compounded semiannually and terminates
with a balance of $5509.39, how long was the money invested for? hint: use table a11 or log calculations

4 yrs

8 yrs

16 yrs

32 yrs

The money was invested for 16 years

Step-by-step explanation:

This is a compound interest problem and the following information has been provided;

Principal, P = 2500

Rate, r = 0.05 compounded semiannually. This will imply an effective rate of 0.05/2 = 0.025 effective per semiannual period.

Accumulated amount, A = 5509.39

We are required to determine the duration of investment in years. We let the number of years be n. We then use the compound interest formula;

We raise to power 2n since there are 2n semiannual periods in n years. The next step is to divide both sides by 2500;

We introduce logs in order to solve for n;

215.92 dollars is the answer

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!