Question

In July 2005, the internet was linked by a global network of about 353 million host computers. The number of host computers has been growing approximately exponentially and was about 37.1 million in July 1998. (a) Find a formula for the number, N, of internet host computers (in millions of computers) as an exponential function of t, the number of years since July 1998, using the continuous exponential model N ( t )

Answer 1

Answer:

$N(t) = 37.1(1.38)^t$

Step-by-step explanation:

Exponential function:

An exponential function has the following format:

$N(t) = N(0)(1+r)^t$

In which N(0) is the initial value and r is the rate of change, as a decimal.

37.1 million in July 1998

This means that $N(0) = 37.1$

So

$N(t) = 37.1(1+r)^t$

In July 2005, the internet was linked by a global network of about 353 million host computers.

This is 2005 - 1998 = 7 years, so $N(7) = 353$. We use this to find r.

$N(t) = 37.1(1+r)^t$

$353 = 37.1(1+r)^7$

$(1+r)^7 = \frac{353}{37.1}$

$\sqrt[7]{(1+r)^7} = \sqrt[7]{\frac{353}{37.1}}$

$1 + r = (\frac{353}{37.1})^{\frac{1}{7}}$

$1 + r = 1.38$

The formula is:

$N(t) = 37.1(1.38)^t$