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.)
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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 27E
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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.
(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.
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.)Expert Solution
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