m 100 operationcond. e Express the number of operations per second N as an exponential function of the time t years since 1940.

Question

In1940, a computer could perform about 100 operations per second. Since then, the speed of computers has multiplied tenfold about every 7 years. Express the number of operations per second N as an exponential function of the time t years since 1940.

Answer 1

 

 N(t) = C*B^t where C is a fixed number constant and B is the base

 

 N(0) = 100    ---->  100 = C*B^(0) ---> C = 100

 

  N(t) = 100*B^t

 

N(7) = 1000 ---->     1000 = 100*B^7

                                  10 = B^7

                                log 10 = log B^7

                                 1 = 7 * log B

                                 1/7 = log B

                                10^(1/7) = B

 

 

N(t) = 100* 10^(t/7)