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Question
\theta =0.4e^{2t}
Function
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Find the inverse
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Evaluate the derivative
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Find the domain
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\text{Find the }t\text{-intercept/zero}
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Find the y-intercept
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Find the critical numbers
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Find the local extrema
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Find the increasing or decreasing interval
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Find the range
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Find the vertical asymptotes
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Find the horizontal asymptotes
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Find the oblique asymptotes
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Determine if even, odd or neither
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Find the stationary points
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Find the inflection points
More methods
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f^{-1}\left(t\right) = \frac{\ln{\left(5\right)}-\ln{\left(2\right)}+\ln{\left(t\right)}}{2}
Evaluate
\theta =0.4e^{2t}
Evaluate
\theta=0.4e^{2t}
\text{Interchange }t\text{ and }y
t=0.4e^{2y}
Swap the sides of the equation
0.4e^{2y}=t
Divide both sides
\frac{0.4e^{2y}}{0.4}=\frac{t}{0.4}
Divide the numbers
e^{2y}=\frac{t}{0.4}
Divide the numbers
More Steps
Evaluate
\frac{t}{0.4}
Convert the decimal into a fraction
More Steps
Evaluate
0.4
Convert the decimal into a fraction
\frac{4}{10}
Reduce the fraction
\frac{2}{5}
\frac{t}{\frac{2}{5}}
Multiply by the reciprocal
t\times \frac{5}{2}
Multiply the terms
\frac{5}{2}t
e^{2y}=\frac{5}{2}t
Take the logarithm of both sides
\ln{\left(e^{2y}\right)}=\ln{\left(\frac{5}{2}t\right)}
Evaluate the logarithm
2y=\ln{\left(\frac{5}{2}t\right)}
Divide both sides
\frac{2y}{2}=\frac{\ln{\left(\frac{5}{2}t\right)}}{2}
Divide the numbers
y=\frac{\ln{\left(\frac{5}{2}t\right)}}{2}
Simplify
More Steps
Evaluate
\ln{\left(\frac{5}{2}t\right)}
\text{Use }\log_{a}(x\times y)=\log_{a}(x)+\log_{a}(y)\text{ to transform the expression}
\ln{\left(\frac{5}{2}\right)}+\ln{\left(t\right)}
\text{Use }\log_{a}(\frac{x}{y})=\log_{a}(x)-\log_{a}(y)\text{ to transform the expression}
\ln{\left(5\right)}-\ln{\left(2\right)}+\ln{\left(t\right)}
y=\frac{\ln{\left(5\right)}-\ln{\left(2\right)}+\ln{\left(t\right)}}{2}
Solution
f^{-1}\left(t\right) = \frac{\ln{\left(5\right)}-\ln{\left(2\right)}+\ln{\left(t\right)}}{2}
Show Solutions
Solve the equation
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\text{Solve for }\theta
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\text{Solve for }t
\theta =\frac{2e^{2t}}{5}
Evaluate
\theta =0.4e^{2t}
Solution
\theta =\frac{2e^{2t}}{5}
Show Solutions
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