What are the bla? Often new technology spreads exponentially. Between 1995 and 2005, each year the number of internet domain hosts was 1.43 times the number of hosts in the preceding year. In 1995, the number of hosts was 8.2 million. a) Explain why the number of hosts is an exponential function of time. The number of hosts grows by a factor of _____ each year, this is an exponential function because the number is growing by constant multiples. b) Find a formula for the exponential function that gives the number N of hosts, in millions, as a function of the time t in years since 1995. N= c) According to this model, in what year did the number of hosts reach 35 million? (Round your answer to the nearest year.)

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odgovoreh · Accepted Answer

Step 1  The problem concerns aspects of an exponential growth model  Step 2  a) blank = constant  (basically geometric series model)  Step 3  b) N(t) expressed as a function of time  (in years since 1995)  b) year 1995↔t=0  year 1996↔t=1, and so on  N(1)=8.2×1.43=8.2×(1.43)1  N(2)=N(1)×1.43=8.2×(1.43)2  In general  N(t)=8.2×(1.43)t  Step 4  c ) the value of t=4 , the nearest year -1999.  c) to solve for t:  35=N(t)=8.2×(1.43)t  (1.43)t=358.2⇒t=ln⁡(358.2)÷ln⁡(1.43)  =4.057…=4  so, the required year = 1999.

What are the blaNSK?Often new technology spreads exponentially. Between 199

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