What is the inverse of f(t)=100(2^{t/3}) ?

The inverse of f(t)=100(2^{t/3}) is (3ln(t/(100)))/(ln(2))

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inverse of f(t)=100(2^{t/3})

inverse

f (t) = 100 (2^{\frac{t}{3}})

\frac{3 ln ( \frac{t}{100} )}{ln ( 2 )}

Solution steps

y = 100 \cdot 2^{\frac{t}{3}}

Replace

t

with

y

t = 100 \cdot 2^{\frac{y}{3}}

Solve for

y, t = 100 2^{\frac{y}{3}}

\frac{3 ln ( \frac{t}{100} )}{ln ( 2 )}

What is the inverse of f(t)=100(2^{t/3}) ?
The inverse of f(t)=100(2^{t/3}) is (3ln(t/(100)))/(ln(2))