The population of a colony of mosquitoes obeys the law of uninhibited growth. Use this information to answer parts (a) through (c). (E (a) If N is the population of the colony and tis the time in days, express N as a function oft. Consider N0 is the original amount att= 0 and k# 0 is a constant that represents the growth rate. NU) = (Type an expression using t as the variable and in terms of e.) (b) The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1900 after 1 day, what is the size of the colony after 4 days? Approximately mosquitoes (Do not round until the final answer. Then round to the nearest whole number as needed.) (c) How long is it until there are 30 ,000 mosquitoes? About days (Do not round until the final answer. Then round to the nearest tenth as needed.) t A mass of 100 grams of a particular radioactive substance decays according to the function m(t) = 100 e 900 , where t>0 measures time in years. When does the mass reach 70 gr: The mass reaches 70 grams aftert= 1 years. (Round to the nearest whole number as needed.) t 'W A mass of 100 grams of a particular radioactive substance decays according to the function m(t) = 100 e , where t>0 measures time in years. When does the mass reach 70 grams? The mass reaches 70 grams aftert= years. (Round to the nearest whole number as needed.) Simplify the complex rational expression. X+4 x + 13 X - 3 X+ 7 x + 67 x +4 X + 13 x - 3 x+ 7 (Type your answer in factored form.) x + 67\fSolve the equation. 3x + 6 4x EX 3 X - 3 . . . 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.) O B. The solution is the empty set.Assume log bx = 0.37, log by = 0.55, and log bz = 0.83. Evaluate. M Z log b w LB log b 2 (Type an integer or a decimal.) Factor completely. If a polynomial cannot be factored, say so. 4x2 - 15x 4 (E Select the correct choice below and, if necessary, ll in the answer box to complete your choice. '3' A' 4X2 - 15x - 4 = (Factor completely.) {:3 B. The polynomial cannot be factored. Find and simplify each of the following for f(x) = 4x - 5x + 9. (A) f(x + h) (B) f(x + h) - f(x) (C) f(x + h) -f(x) h (A) f(x + h) =| (Do not factor.) (B) f(x + h) - f(x) = (Do not factor.) (C) f ( x + h) - f(x) = (Do not factor.) hSolve the equation on the interval 0 S B