Answer:
[tex]N(t) = 37.1(1.38)^t[/tex]
Step-by-step explanation:
Exponential function:
An exponential function has the following format:
[tex]N(t) = N(0)(1+r)^t[/tex]
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 [tex]N(0) = 37.1[/tex]
So
[tex]N(t) = 37.1(1+r)^t[/tex]
In July 2005, the internet was linked by a global network of about 353 million host computers.
This is 2005 - 1998 = 7 years, so [tex]N(7) = 353[/tex]. We use this to find r.
[tex]N(t) = 37.1(1+r)^t[/tex]
[tex]353 = 37.1(1+r)^7[/tex]
[tex](1+r)^7 = \frac{353}{37.1}[/tex]
[tex]\sqrt[7]{(1+r)^7} = \sqrt[7]{\frac{353}{37.1}}[/tex]
[tex]1 + r = (\frac{353}{37.1})^{\frac{1}{7}}[/tex]
[tex]1 + r = 1.38[/tex]
The formula is:
[tex]N(t) = 37.1(1.38)^t[/tex]
