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If the equation y=5(1.7)^x is plotted on a semi-log scale graph, then the linearized equation will be log(y)=mx+b, where m=_____?_____ and b=____?_____.

2 Answers

13 votes

Answer:

m=1.7 and b=5

Explanation:

5= the y intercept

1.7= the slope that's why it has x as its exponent. Because in mx+b the slope is the one that keeps being multiplied.

User Teratorn
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13 votes

In the linearized equation log(y) = mx + b, m=log(1.7) and b=log(5).

In the equation y = mx + b, the 'm' represents the slope of the line, while the 'b' represents the y-intercept. To determine the values of 'm' and 'b' for the linearized equation log(y) = mx + b, we need to convert the original equation from exponential form to logarithmic form.

First, take the logarithm of both sides of the equation: log(y) = log(5(1.7)ˣ). We can use the logarithmic property log(ab) = log(a) + log(b) to simplify further: log(y) = log(5) + log(1.7ˣ). Since log(1.7ˣ) = x*log(1.7), the equation becomes: log(y) = log(5) + x*log(1.7). Comparing with the linearized equation log(y) = mx + b, we can see that 'm' is equal to log(1.7) and 'b' is equal to log(5).

COMPLETE QUESTION:

If the equation y=5(1.7) ˣ is plotted on a semi-log scale graph, then the linearized equation will be log(y)=mx + b, where m=_____? _____ and b=____? _____.

User Lambder
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3.8k points