What is the answer to 200=1000-1000(0.9)^t ?

The answer to 200=1000-1000(0.9)^t is t=(ln(4/5))/(ln(0.9))

Solve for t: 200=1000-1000(0.9)^t

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

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200 = 1000 - 1000 (0.9)^{t}

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

Decimal Notation

t = 2.11790 \dots

Solution steps

200 = 1000 - 1000 (0.9)^{t}

Switch sides

1000 - 1000 \cdot 0. 9^{t} = 200

Move

1000

to the right side

- 1000 \cdot 0. 9^{t} = - 800

Divide both sides by

- 1000

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 )}

2 \cdot 1 1^{x} - 4 = 452

3^{2 x + 1} - 2 7^{x} = 0

\frac{3}{5 ^{x}} = 0.12

3^{x + 2} + 9^{x + 1} = 108

130 = 52 e^{k \cdot 20}

What is the answer to 200=1000-1000(0.9)^t ?
The answer to 200=1000-1000(0.9)^t is t=(ln(4/5))/(ln(0.9))
Solve for t: 200=1000-1000(0.9)^t
The solution is t=(ln(4/5))/(ln(0.9))