help me figure this out please

Question

The current through a particular wire can be modeled by I(t) = 2t2 − 6t + 7 where I(t) is the current in amperes after t seconds. (a) Find the current in the wire after 0.5 seconds. The current in the wire after 0.5 seconds would be about amperes. (b) After how many seconds would the current reach 15 amperes? (Round your answer to two decimal places. Include units with your numerical answers.) After about the current would reach 15 amperes. (c) After how many seconds would the current reach 30 amperes? (Round your answer to two decimal places. Include units with your numerical answers.) After about the current would reach 30 amperes.

Answer 1

A) I(0.5) = 2(O.5)² - 6(0.5) + 7 = 4.50 A

 

B)     15  = 2t² - 6t +7  REARRANGE THIS TO:  2t² - 6t - 8 = 0 OR t² - 3t - 4 = 0 (divided by 2)

     THIS IS A QUADRATIC EQUATION THAT FACTORS INTO (t - 4)(t + 3) = 0

 

SO t = 4, or -3 YOU CAN'T HAVE A NEGATIVE TIME, SO t = 4 sec

 

C)    30 = 2t² - 6t +7 REARRANGE THIS TO 2t² - 6t - 23 = 0

 

THIS WON'T FACTOR, SO IT CAN BE SOLVED USING THE QUADRATIC FORMULA:

 

t = 6 +/- √(-6)²  - 4(2)(-23)/2(2)  =  (6 +/- √220)/ 4 = 5.21 SEC (OR -2.21 SEC, BUT IT CAN'T BE NEGATIVE)