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Solve for x to the nearest 10th.

3000=6680(0.985)^(x)-1200

Solve for $x$ to the nearest $10$ th. $\newline$ $3000=6680(0.985)^{x}-1200$

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Find trigonometric functions using a calculator

Full solution

Q. Solve for

x

to the nearest

10

th.

\newline

3000=6680(0.985)^{x}-1200

Set up equation: Set up the equation given by the problem. $\newline$ $3000 = 6680(0.985)^x - 1200$
Addition and isolation: Add $1200$ to both sides to isolate the exponential term on one side. $\newline$ $3000 + 1200 = 6680(0.985)^x$ $\newline$ $4200 = 6680(0.985)^x$
Divide to solve: Divide both sides by $6680$ to solve for $(0.985)^x$ . $\newline$ $\frac{4200}{6680} = (0.985)^x$ $\newline$ $0.628742515 = (0.985)^x$
Take natural logarithm: Take the natural logarithm of both sides to solve for $x$ . $\ln(0.628742515) = \ln((0.985)^x)$ $\ln(0.628742515) = x \cdot \ln(0.985)$
Divide by $\ln(0.985)$ : Divide both sides by $\ln(0.985)$ to solve for $x$ .
$x = \frac{\ln(0.628742515)}{\ln(0.985)}$
$x \approx \frac{\ln(0.628742515)}{\ln(0.985)}$
$x \approx \frac{-22.34434768}{-0.015113296}$
$x \approx 1478.577855$

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