The number of research articles in a prominent journal written by researchers during 1983–2003 can be approximated by U(t) = 4.1e0.6t 0.2 + e0.6t thousand articles per year (0 ≤ t ≤ 20) where t is time in years (t = 0 represents 1983). (a) Find an (approximate) expression for the total number of articles (in thousands) written since 1983 (t = 0). HINT [See Example 5.] (Round your coefficients to two decimal places.) N(t) = (b) Roughly how many articles were written from 1983 to 2003? (Round your answer to the nearest whole number.) thousand articles

Step-by-step explanation:

From the information given:

We are to find; an expression for the total no. of articles written since 1983

∴

The total no. of articles written since 1983  

Therefore, the total number of articles written since 1983 is  

b. To find how many articles were being written  from 1983 to 2003

i.e. t = 2003 - 1983 = 20

∴

Total articles written from 1983 to  2003 is

= 80.75 thousand articles

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

replace   with   27   and simplify.

10 , 27 , 10 , 70 , 10 , 35 , 10 , 48

step-by-step explanation: