Question

Solve for t in the equation 67 = 19e^(0.07t).

Answer 1

To solve for t in the equation 67 = 19e^(0.07t), we can follow these steps:

1. Start with the equation 67 = 19e^(0.07t).

2. Divide both sides of the equation by 19 to isolate the exponential term:

67/19 = e^(0.07t).

3. Simplify the left side of the equation:

3.5263 ≈ e^(0.07t).

4. Take the natural logarithm (ln) of both sides to eliminate the exponential:

ln(3.5263) ≈ ln(e^(0.07t)).

5. Use the property of logarithms that ln(e^x) = x:

ln(3.5263) ≈ 0.07t.

6. Divide both sides of the equation by 0.07 to solve for t:

ln(3.5263) / 0.07 ≈ t.

7. Use a calculator to evaluate the left side of the equation:

t ≈ ln(3.5263) / 0.07 ≈ 9.8537.

Therefore, t is approximately equal to 9.8537 when solving the equation 67 = 19e^(0.07t).

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Answer 2

To solve for t in the given equation, we can use logarithms to isolate t and then divide to find the final answer.

Step-by-step explanation:

To solve for t in the equation 67 = 19e^(0.07t), we can take the natural logarithm of both sides to eliminate the exponential term. This will give us:

ln(67) = ln(19) + 0.07t

Next, we can isolate t by subtracting ln(19) from both sides:

ln(67) - ln(19) = 0.07t

Finally, we can divide both sides by 0.07 to solve for t:

t = (ln(67) - ln(19))/0.07