The population of a colony of mosquitoes obeys the law of uninhibited growth. Use this information to answer parts (a) through (c). (a) IT IN is the population of the colony and t is the time in days, express IN as a function of t. Consider No Is the original amount at t=U and KFU is a constant that represents the growth rate. N(t)=Noe kt (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 1200 after 1 day, what is the size of the colony after 4 days? Approximately 2074 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 20,000 mosquitoes? D About days not round until the final answer. Then round to the nearest tenth as needed.)