# 1.sketch the graph y=3^x 2.sketch the graph of y=(1/5)^x Evaluate the following exponential expressions. 3. (2^3)^3 4. (5)^2(5)^3 5.Write your answer using a radical. (2^1/4)(3^1/4)

1.sketch the graph y=3^x 2.sketch the graph of y=(1/5)^x Evaluate the following exponential expressions. 3. (2^3)^3 4. (5)^2(5)^3 5.Write your answer using a radical. (2^1/4)(3^1/4) 6. 7^2 / 7^5 7. (2/3)^4 8.If f(x) = 7^x(^2-x) , find all the values of x such that f(x)=48. 9.Suppose $900 is invested at an annual interest rate of 4% for a period of 15 years. Compute the future value of the investment if interest is compounded quarterly. Round your final answer to the nearest cent and intermediate calculations to four decimal places. 10. Suppose $1,000 is invested at an annual rate of 6% for a period of 9 years. Compute the future value of the investment if interest is compounded monthly. Round your final answer to the nearest cent and intermediate calculations to four decimal places. Evaluate 11. log9 (729) 12. log8 (64) 13. log2 (1/8) Solve the following equations for x: 14. log27 (x)=1/3 15. log27 (9)=x 16. logx (9)=2 17. Use logarithm rules to rewrite the following expression in terms of log8(5)… log8 (8/5) 18. Use logarithm rules to rewrite the following expression in terms of log9 (5) and log9 (2)….. log9 (1,000) 19.Use the logarithm rules to expand the following expression. log4 (y^7 /x^4) Differentiate the functions 20. f(x) = e^x^5 + 3 21. f(x) = (e^-3x) / (x^2 +9) 22. Find the largest and smallest values of the funstion f(x) = xe^2x on the interval -2 ≤ x ≤ 3. Round your answer to three decimal places. Differentiate the functions 23. f(x) = x^6 ln x 24. f(x) = (ln ^8√x^5) / (x^5) 25. f(x) = (^6√x+6) / (6-8x)^8 26. A manufactuerer determines that x units of a particular luxury item will be sold when the price is p(x) = 129 -x ln (√x) hundred dollars per unit. Find the revenue and marginal revenue as functions of the number of units produced and sold. 27. Sketch the graph of f(x) = x^2 -50 ln x 28. Barotolo owns a parcel of land whose market value t years from now is estimates to be V(t) = 11,000e^√t dollars. If prevailing interest rate remains constant at 12% compounded continuously, when should Bartolo sell if his goal is to maximize the present value of the investment? round your final answer to the nearest year. 29. Public health records indicate that t weeks after the outbreak of a certain form of influenza, approximately Q(t) = 17 / (1+16e^-1.3t) thousand people had caught the disease. How many people had the disease when it broke out? 30. Suppose that for a particular semelparous organism, the likelihood of an individual surviving to a age x (years) is given by p(x) = e^-0.15x and that the number of female births at age x is f(x) = 2x^0.94. What is the optimal age for reproduction? Round your intermediate calculations and the final answer to four decimal places.