Please show me step-by-step processes?Thanks. The number of applications for patents, N. grew dramatically in recent yoars, with growth averaging about 4.4% per year. That is, N'(1) - 0.044N(1).a)Find the function that satisfies this equation. Assume that t=0 corresponds to 1980, when approximately 120,000 patent applications were received.b)Estimate the number of patent applications in 2015.c)Estimate the doubling time for N(t).a) Choose the correct answer below.A. N(t) = 120,.000 e00441%3DOB. N(t) = 120.0000 044 eOC. N'(1) - 120,000 e00441O D. N(t) = 0.044 e 120,0001b) The number of patent applications in 2015 will be(Do not round until the final answer. Then round to the nearest integer as needed.)Enter your answer in the answer box and then click Check Answer.1 partremainingClear AllstartP Type here to search6.DELLF2FBF9F10EscF1F3F4FSF6F7

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The number of applications for patents, N. grew dramatically in recent years, with growth averaging about 4.4% per year. That is, N'(t) = 0.044N(t). Find the function that satisfies this equation. Assume that t= 0 corresponds to 1980, when approximately 120.000 patent applications were received. b) Estimate the number of patent applications in 2015. Estimate the doubling time for N(t).