Hello! I'm putting together a study guide for my final and I need help with these 10 questions as I'm struggling with understanding them. I included attachments of them in order!

After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1997, the hay in that country was contaminated by a radioactive isotope (half-life 8 days). If it is safe to feed the hay to cows when 15% of the radioactive isotope remains, how long did the farmers need to wait to use this hay? The farmers needed to wait approximately days for it to be safe to feed the hay to the cows. (Round to one decimal place as needed.) #The population of a southern city follows the exponential law. Use this information to answer parts a and b. (a) If N is the population of the city and t is the time in years, express N as a function of t. N(t) = (Type an expression using t as the variable and in terms of e.) (b) If the population doubled in size over 21 months and the current population is 10,000, what will the population be 4 years from now? The population will be approximately | people. (Do not round until the final answer. Then round to the nearest whole number as needed.)If Tanisha has $100 to invest at 6% per annum compounded quarterly, how long will it be before she has $150? If the compounding is continuous, how long will it be? Compounding quarterly, it will be about |years before Tanisha has $150. (Round to two decimal places as needed.) Compounding continuously, it will be about years before Tanisha has $150. (Round to two decimal places as needed.) # 3Uninhibited growth can be modeled by exponential functions other than A(t) =Ap ek. For example, if an initial population Po requires n units of time to triple, then the function P(t) = Po(3)" models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below. (a) If the population triples in 20 days, and 60 insects are present initially, write an exponential function of the form P(t) = Po(3) " that models the population. P(t) = (b) What will the population be in 47 days? The population in 47 days will be (Round to the nearest integer as needed.) # L (c) When will the population reach 960? The population will reach 960 in days (Round to one decimal place as needed.) (d) Express the model from part (a) in the form A(t) = Ap e Kt P(t) = (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)Solve the following exponential equation. Express irrational solutions in exact form. 2 .81% + 3.9* + 7=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The solution set is (Simplify your answer. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.) O B. There is no solution.Find the principal needed now to get the given amount; that is, find the present value. To get $900 after 4 years at 4% compounded quarterly The present value of $900 is $ (Round to the nearest cent as needed.) Enter your answer in the answer box.Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool decomposes according to the law of uninhibited decay. After shocking a pool, the pool boy, Geoff, tested the water and found the amount of free chlorine to be 2.3 parts per million (ppm). Twenty-four hours later, Geoff tested the water again and found the amount of free chlorine to be 1.9 ppm. What will be the reading after 3 days (that is, 72 hours)? When the chlorine level reaches 1.0 ppm, Geoff must shock the pool again. How long can Geoff go before he must shock the pool again? After 3 days, or 72 hours, the amount of free chlorine in the pool will be ppm. (Do not round until the final answer. Then round to the nearest hundredth as needed.) Geoff will need to shock the pool again in hours (Do not round until the final answer. Then round to the nearest tenth as needed.)Solve the following logarithmic equation. log x + log (x + 15)=2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.) O B. There is no solution. # 8Solve the exponential equation. Express irrational solutions in exact form. 8x -5 =64 What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { (Simplify your answer. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.) O B. There is no solution. # 9What rate of interest compounded annually is required to triple an investment in 11 years? The rate of interest required is% (Round to two decimal places as needed.)