10. objective: solve applied problems involving exponential functions and their graphs (optional)…

10. objective: solve applied problems involving exponential functions and their graphs (optional) corresponding textbook exercises: 51 - 76 sample problem: 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 where t is the number of years after 1984, can 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.

10. objective: solve applied problems involving exponential functions and their graphs (optional) corresponding textbook exercises: 51 - 76 sample problem: 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 where t is the number of years after 1984, can 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.

Answer

Explanation:

Step1: Calculate the value of (t) for 1995

For 1995, (t = 1995 - 1984=11).

Step2: Substitute (t = 11) into the function

Substitute (t = 11) into (M(t)=7.91477(1.26698)^{t}), we get (M(11)=7.91477(1.26698)^{11}). First, calculate ((1.26698)^{11}\approx13.497). Then (M(11)=7.91477\times13.497\approx106.92\approx107) MHz.

Step3: Calculate the value of (t) for 2009

For 2009, (t = 2009 - 1984 = 25).

Step4: Substitute (t = 25) into the function

Substitute (t = 25) into (M(t)=7.91477(1.26698)^{t}), we get (M(25)=7.91477(1.26698)^{25}). First, calculate ((1.26698)^{25}\approx119.77). Then (M(25)=7.91477\times119.77\approx947.96\approx948) MHz.

Answer:

The CPU - power of a Macintosh Performa 5320CD in 1995 is approximately 107 MHz and of an iMac G6 in 2009 is approximately 948 MHz.