1100=700(1+(00.2)/(12))^(12 t)

Isolate exponential part: First, let's isolate the exponential part of the equation by dividing both sides by 700. 1100 / 700 = (1 + (0.2 / 12))^(12 * t)Calculate left side: Now, let's calculate the left side of the equation. 1100 / 700 = 1.57142857...Take natural logarithm: Next, we need to take the natural logarithm (ln) of both sides to solve for t. ln(1.57142857...) = ln((1 + (0.2 / 12))^(12 * t))Rewrite right side: Using the property of logarithms that ln(a^b) = b * ln(a), we can rewrite the right side of the equation. ln(1.57142857...) = 12 * t * ln(1 + (0.2 / 12))Calculate natural logarithm: Now, let's calculate the natural logarithm of both sides. ln(1.57142857...) ≈ 0.45107562 ln(1 + (0.2 / 12)) ≈ ln(1.01666667...) ≈ 0.01652943Solve for t: We can now solve for t by dividing both sides by 12 * ln(1 + (0.2 / 12)). t = ln(1.57142857...) / (12 * ln(1 + (0.2 / 12))) t ≈ 0.45107562 / (12 * 0.01652943)Calculate value of t: Finally, let's calculate the value of t. t ≈ 0.45107562 / (12 * 0.01652943) t ≈ 0.45107562 / 0.19835316 t ≈ 2.274

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$1100=700\left(1+\frac{00.2}{12}\right)^{12 t}$

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1100=700\left(1+\frac{00.2}{12}\right)^{12 t}

Isolate exponential part: First, let's isolate the exponential part of the equation by dividing both sides by $700$ . $\newline$ $\frac{1100}{700} = \left(1 + \frac{0.2}{12}\right)^{12 \cdot t}$
Calculate left side: Now, let's calculate the left side of the equation. $\frac{1100}{700} = 1.57142857\ldots$
Take natural logarithm: Next, we need to take the natural logarithm ( $\ln$ ) of both sides to solve for $t$ . $\ln(1.57142857\ldots) = \ln\left((1 + (0.2 / 12))^{12 \cdot t}\right)$
Rewrite right side: Using the property of logarithms that $\ln(a^b) = b \times \ln(a)$ , we can rewrite the right side of the equation. $\ln(1.57142857\ldots) = 12 \times t \times \ln(1 + (\frac{0.2}{12}))$
Calculate natural logarithm: Now, let's calculate the natural logarithm of both sides. $\newline$ $\ln(1.57142857...) \approx 0.45107562$ $\newline$ $\ln(1 + (0.2 / 12)) \approx \ln(1.01666667...) \approx 0.01652943$
Solve for t: We can now solve for $t$ by dividing both sides by $12 \times \ln(1 + (0.2 / 12))$ .
$t = \frac{\ln(1.57142857...)}{12 \times \ln(1 + (0.2 / 12))}$
$t \approx \frac{0.45107562}{12 \times 0.01652943}$
Calculate value of t: Finally, let's calculate the value of $t$ . $t \approx \frac{0.45107562}{12 \times 0.01652943}$ $t \approx \frac{0.45107562}{0.19835316}$ $t \approx 2.274$