The central processing unit (CPU) power in computers has increased significantly over the years. The CPU power in Macintosh computers has grown exponentially from 8 MHz in 1984 to 3400 MHz in 2013 (Source: Apple. The exponential function $M(t)=7.91477(1.26698)^t[math], where t is the number of years after 1984, an be used to estimate the CPU power in a Macintosh computer in a given year. Find the CPU power of a Macintosh Performa 5320CD in 1995 and of an iMac G6 in 2009. Round to the nearest one MHz.

The central processing unit (CPU) power in computers has increased significantly over the years. The CPU power in Macintosh computers has grown exponentially from 8 MHz in 1984 to 3400 MHz in 2013 (Source: Apple. The exponential function $M(t)=7.91477(1.26698)^t[math], where t is the number of years after 1984, an be used to estimate the CPU power in a Macintosh computer in a given year. Find the CPU power of a Macintosh Performa 5320CD in 1995 and of an iMac G6 in 2009. Round to the nearest one MHz.

Question
Exponents and radicals
asked 2021-01-08
The central processing unit (CPU) power in computers has increased significantly over the years. The CPU power in Macintosh computers has grown exponentially from 8 MHz in 1984 to 3400 MHz in 2013 (Source: Apple. The exponential function \(\displaystyle\${M}{\left({t}\right)}={7.91477}{\left({1.26698}\right)}^{{t}}{\left[{m}{a}{t}{h}\right]}\), where t is the number of years after 1984, an be used to estimate the CPU power in a Macintosh computer in a given year. Find the CPU power of a Macintosh Performa 5320CD in 1995 and of an iMac G6 in 2009. Round to the nearest one MHz.

Answers (1)

2021-01-09

For Macintosh Perfoma 5320CD, substitute \(t=1995-1984=11\),

\(M(11)=7.91477(1.26698)^{11}\)

Use a calculator: \(\displaystyle{M}{\left({11}\right)}\sim{106.88}\to\)107MHz

For iMac G6, substitute \(t=2009-1984=25\),

\(\displaystyle{M}{\left({25}\right)}={7.91477}{\left({1.26698}\right)}^{{25}}\)

Use a calculator: \(\displaystyle{M}{\left({25}\right)}\sim{2935.50}\to\) 2936MHz

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