More and more businesses and homeowners are installing solar panels on their roofs to draw energy from the sun's rays. According to the U. S. Department of Energy, the solar cell kilowatt-hour use in the United States (in millions) is projected to be S(t) = 0.73t2 + 15.8t +2.7 (0 < t < 8) in year t, with t = 0 corresponding to 2000. What was the number of projected solar cell kilowatt-hours used in the United States for 2001? For 2002?

S(2001) = 19.23

S(2002) = 37.22

Step-by-step explanation:

Given that;

S(t) = 0.73t^2 + 15.8t +2.7

t = 0 corresponding 2000

t = 1 then, its mean year 2001

so

S(2001) = 0.73(1)^2 + 15.8(1) +2.7

= 0.73 + 15.8 + 2.7

S(2001) = 19.23

also

t = 2 then, it means 2002

so

S(2002) = 0.73(2)^2 + 15.8(2) +2.7

= 2.92 + 31.6 + 2.7

S(2002) = 37.22

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}