A = FV - OV/T for OV
2 answers:
Starting with the equation:
Isolate OV.
Eliminate the denominator by multiplying every term by T
Now move OV to the right-hand side by adding it to both sides
Subtract A*T from both sides
Simplify the expression
Hence,
Thus the solution is
Isolate OV to obtain OV = T(FV - a)
Additional explanation
Statements that assert two expressions are equal are referred to as equations
Linear equations are open statements involving variables in which each variable appears with an exponent of one
A single-variable linear equation contains one variable raised to the first power and can be expressed as:
ax = b or ax + b = c,
in which
a, b, and c are constants, and x represents the variable
By contrast, a two-variable linear equation includes two variables, both to the first power
It can be written in the form:
ax + by = c
x and y are variables
Common methods for solving linear equations
- 1. substitution and elimination
- 2. adding or subtracting the same quantity to both sides
- 3. multiplying or dividing both sides by the same nonzero number
- 4. using a graph
For this problem, the given linear relation is:
a = FV - OV/T
We will apply techniques 2 and 3 from the list above
- method 3
Multiply both sides of the equation by T to remove the fraction:
aT= FVT - OV
- method 2
Add OV to both sides:
aT + OV = FVT
Then isolate OV by relocating aT to the opposite side.
OV = FVT - aT
OV = T(FV-a)
Read further
Three times b is less than 100
two-variable linear equation examples
James is 2 years younger
Keywords: one variable, linear equation, two-variable, constants, x variable, y variable, exponent
You might be interested in
Answer:
After five years beyond the initial 20-year stretch, the population of this small community will be 4268.
Step-by-step explanation:
t | 0 | 5 | 10 | 15 | 20
p | 100 | 200 | 450 | 950 | 2000
The representation of the exponential function is:
p = aeᵏᵗ
where a and k represent constants.
Taking the natural logarithm on both sides:
In p = In aeᵏᵗ
In p = In a + In eᵏᵗ
In p = In a + kt
In p = kt + In a.
We can apply linear regression to model the relationship between In p and t, thereby determining the values of k and In a.
t | 0 | 5 | 10 | 15 | 20
p | 100 | 200 | 450 | 950 | 2000
In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601
In p = kt + In a.
y = mx + b
Here m corresponds to k and b is In a
By conducting a linear regression on the transformed linear relationship among In p and t and creating a graph of the variables, we derive the regression equation:
y = 0.151x + 4.584
The first image illustrates the equations needed for estimating the parameters of linear regression.
The second image displays the regression calculations alongside the graph of In p versus t.
By comparing
y = 0.151x + 4.584
to
In p = kt + In a.
y = In p
k = 0.151
x = t
In a = 4.584
a = 97.905
Thus, the exponential relationship between p and t is formulated as:
p = 97.905 e⁰•¹⁵¹ᵗ
In order to forecast the population for 5 years ahead from the 20-year mark, we need to find p at t=25 years.
0.151 × 25 = 3.775
p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41, which rounds down to 4268.
Hope this assists!!!
