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If the equation y = aebx can be written in linear form Y = A + BX, what are Y, X, A, B?
- a)Y = logy, A = loga, B=b and X=x
- b)Y = y, A = a, B=b and X=x
- c)Y = y, A = a, B=logb and X=logx
- d)Y = logy, A = a, B=logb and X=x
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the equation y = aebx can be written in linear form Y = A + BX, wha...
The equation is
y = aebx.
Taking log to the base e on both sides,
we get logy = loga + bx.
Which can be replaced as Y = A+BX,
where Y = logy, A = loga, B = b and X = x.
y = aebx.
Taking log to the base e on both sides,
we get logy = loga + bx.
Which can be replaced as Y = A+BX,
where Y = logy, A = loga, B = b and X = x.
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Community Answer
If the equation y = aebx can be written in linear form Y = A + BX, wha...
To understand why option 'A' is the correct answer, let's break down the given equation and the linear form.
Given equation: y = aebx
Linear form: Y = A BX
Now, let's analyze each variable in the given equation and the linear form.
1. Variable 'y':
In the given equation, 'y' represents the dependent variable, which is usually the output or the response variable.
2. Variable 'a':
In the given equation, 'a' represents a constant. It is the initial value of 'y' when 'x' is zero. This constant determines the vertical shift of the graph.
3. Variable 'b':
In the given equation, 'b' represents the rate of change. It determines the steepness or the slope of the graph.
4. Variable 'x':
In the given equation, 'x' represents the independent variable, which is usually the input or the explanatory variable.
Now, let's compare the given equation with the linear form.
Comparing the given equation (y = aebx) with the linear form (Y = A BX), we can see that the variables 'Y' and 'X' in the linear form correspond to 'y' and 'x' in the given equation, respectively.
Therefore, the correct option is 'A' because it correctly identifies the variables in the linear form as:
- Y = logy (corresponding to 'y')
- A = loga (corresponding to 'a')
- B = b (corresponding to 'b')
- X = x (corresponding to 'x')
This interpretation is consistent with the given equation y = aebx, where 'a' and 'b' are constants, and 'x' is the independent variable. The logarithmic form in option 'A' accurately represents the exponential relationship between 'y' and 'x'.
Given equation: y = aebx
Linear form: Y = A BX
Now, let's analyze each variable in the given equation and the linear form.
1. Variable 'y':
In the given equation, 'y' represents the dependent variable, which is usually the output or the response variable.
2. Variable 'a':
In the given equation, 'a' represents a constant. It is the initial value of 'y' when 'x' is zero. This constant determines the vertical shift of the graph.
3. Variable 'b':
In the given equation, 'b' represents the rate of change. It determines the steepness or the slope of the graph.
4. Variable 'x':
In the given equation, 'x' represents the independent variable, which is usually the input or the explanatory variable.
Now, let's compare the given equation with the linear form.
Comparing the given equation (y = aebx) with the linear form (Y = A BX), we can see that the variables 'Y' and 'X' in the linear form correspond to 'y' and 'x' in the given equation, respectively.
Therefore, the correct option is 'A' because it correctly identifies the variables in the linear form as:
- Y = logy (corresponding to 'y')
- A = loga (corresponding to 'a')
- B = b (corresponding to 'b')
- X = x (corresponding to 'x')
This interpretation is consistent with the given equation y = aebx, where 'a' and 'b' are constants, and 'x' is the independent variable. The logarithmic form in option 'A' accurately represents the exponential relationship between 'y' and 'x'.
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If the equation y = aebx can be written in linear form Y = A + BX, what are Y, X, A, B?a)Y = logy, A = loga, B=b and X=xb)Y = y, A = a, B=b and X=xc)Y = y, A = a, B=logb and X=logxd)Y = logy, A = a, B=logb and X=xCorrect answer is option 'A'. Can you explain this answer?
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