5. 4 points Cr 4.1.Ex.018 My Notes Often new technology spreads exponentially. B

Question

5. 4 points Cr 4.1.Ex.018 My Notes 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 an exponential function because the number is growing by Increasing multiples. each year, this is (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. (c) According to this model, in what year did the number of hosts reach 70 million? (Round your answer to the nearest year.) Need Help?ReadItTalk to Tutor Submit Answer Save Progress Practice Another Version

Explanation / Answer

each year number of internet domain is 1.43 times the number of preceding year

so , number if hosts grows by a factor of 1.43 each year

b) initial value = 8.2 million

next year it would be 8.2*1.43

so , formula can be written as

8.2 ( 1.43 ) ^x

N = 8.2 ( 1.43)^x

where x is the number of years since 1995

c) 70 = 8.2 ( 1.43)^x

70/8.2 = 1.43^x

x = 6

so, hosts reach 70 million by 2001

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