1. Solve the equation for x, accurate to three decimal places: ln(x + e) − ln(x − e) = 1. x = 7.389 x = 2.718 x = −2.718 x = 5.882 2. If the half-life of K-40 is 1.3 billion years, approximate the age of a sample rock on the island that has 90.75% of its parent K-40 remaining. The rock is approximately 1.82 × 1011 years old. The rock is approximately 182,040 years old. The rock is approximately 182,039,587 years old. The rock is approximately 8,454,973,459 years old. 3. Solve the equation for x, accurate to three decimal places: e^x−2 + 4 = 91. x = 6.466 x = 2.466 x = 6.443 x = 2.233 4. Solve the equation for x, accurate to three decimal places: e^4x + 5e^2x = 36. x = 2.773 x = 0.693 x = 1.099 x = 1.504 5. Solve the equation for x, accurate to three decimal places: e^2x − 5e^x = 24. x = 1.099 x = 2.079 x = 1.1 x = 2.08 6. Find a best fit exponential regression model to model the data in the table provided, where x represents the input and y represents the output. Round your numerical values to the hundredths decimal place. x 1 2 3 4 5 y 200 98 51 22 11 y = 4.87 ⋅ (0.48)^x y = 423.79 ⋅ (0.48)^x y = 423.80 ⋅ (0.50)^x y = 4.87 ⋅ (0.99)^x 7. If the half life of Pb-210 is 22 years. How much of the original amount of Pb-210 remains after 88 years? 50% 25% 6.25% 12.5% 8. Solve the equation for x, accurate to three decimal places: e^4x − e^2x = 12. x = 1.280 x = 0.693 x = 1.866 x = 0.549 9. Solve the equation for x, algebraically: log sub2(x) − log sub2(x − 2) = 3. x=4 x=2 x=16/7 x=12/5