What is the answer to 280=1400-1400(0.9)^t ?

The answer to 280=1400-1400(0.9)^t is t=(ln(4/5))/(ln(0.9))

Solve for t: 280=1400-1400(0.9)^t

The solution is t=(ln(4/5))/(ln(0.9))

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280 = 1400 - 1400 (0.9)^{t}

t = \frac{ln ( \frac{4}{5} )}{ln ( 0.9 )}

Decimal Notation

t = 2.11790 \dots

Solution steps

280 = 1400 - 1400 (0.9)^{t}

Switch sides

1400 - 1400 \cdot 0. 9^{t} = 280

Move

1400

to the right side

- 1400 \cdot 0. 9^{t} = - 1120

Divide both sides by

- 1400

0. 9^{t} = \frac{4}{5}

Apply exponent rules

t ln (0.9) = ln (\frac{4}{5})

Solve

t ln (0.9) = ln (\frac{4}{5}) : t = \frac{ln ( \frac{4}{5} )}{ln ( 0.9 )}

t = \frac{ln ( \frac{4}{5} )}{ln ( 0.9 )}

3^{x} = 33

200 e^{0.063 t} = 600

3 (2^{x + 4}) = 350

e^{- 3 t} = 0

e^{- 2 x} = (e^{5})^{x + 7}

What is the answer to 280=1400-1400(0.9)^t ?
The answer to 280=1400-1400(0.9)^t is t=(ln(4/5))/(ln(0.9))
Solve for t: 280=1400-1400(0.9)^t
The solution is t=(ln(4/5))/(ln(0.9))