Researchers at the Centers for Disease Control and Prevention have been studying the decay pattern of a new virus with a decay rate of 19% per hour. They start with 300 viruses that they want to check on in the next 7 hours. How many viruses will they find in 7 hours? Round your answer to the nearest whole number

Using an exponential function, it is found that they will find 69 viruses in 7 hours.

A decaying exponential function is modeled by:

In which:

In this problem:

Then

In 7 hours:

They will find 69 viruses in 7 hours.

A similar problem is given at link

The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.

Step-by-step explanation:

The given is,

                     A new virus with a decay rate of 19% per hour  

                    They start with 300 viruses

Step:1

                  Formula to calculate the viruses at decay rate,

                                                  ............................(1)

                 Where, y - No of viruses after given time

                             A - Viruses at initial stage

                              r - Decay rate

                              t - No. of hours

                 From the given,

                              A = 300

                               r = 19% per hour

                               t = 7 hours

                Equation (1) becomes,

               Viruses of 7 hours ≅ 69 viruses

                                                     ( or )

Step:1

        For 1st hour,

          = (No.of viruses in hour) - (No,of viruses in last hour × Decay rate )

              = (300)-(300 × 0.19)

              = 300 - 57

              = 243

       For 2nd hour,

              = (243)-(243 × 0.19)

              = 243 - 46.17

              = 196.83

      For 3rd hour,

              = (196.83)-(196.83 × 0.19)

              = 196.83 - 37.39

              = 159.4323

       For 4th hour,

              = (159.4323)-(159.4323 × 0.19)

              = 159.4323 - 30.2921

              = 129.1402

      For 5th hour,

              = (129.1402)-(129.1402 × 0.19)

              = 129.1402 - 24.5366

              = 104.6035

     For 6th hour,

              = ( 104.6035)-( 104.6035 × 0.19)

              =  104.6035 - 19.8747

              = 84.7288

     For 7th hour,

              = (84.7288)-(84.7288 × 0.19)

              =  84.7288 - 16.0984

              = 68.63 viruses

Result:

          The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.

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step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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