CPhill

Here is the graph of the given function and its parent.......along with the graph of y = 1000000...

https://www.desmos.com/calculator/th77072kjr

The given function rises much less steeply than the parent function, e^t...... [largely because the exponent constant on  e  is much less than 1]....

At L(80), [ the year 2040], the concentration level per million will be about 500 parts per million

In 2015, t = 55, and the concentration level per million was about 406 ppm

The graph cannot be used for all t, because for all t >  458 , the ppm count will exceed 1 million, which is impossible.....thus....this model will be invalid after the year 2418 [approx.]

1/4  of 2/3  =

1/4 * 2/3  =

2/12  =

1/6   of the book was read

lbs . purchased   x   cost per lb.  = total cost

2.5      x    $7.70    =  $19.25

6 × 10^3+3 ×10^2  =

(6 x 1000 ) +  ( 3 x 100 )  =

6000 +  300  =

6300

Here's the graph : https://www.desmos.com/calculator/qgngrhqfqf

To find the x-intercept....let y = 0   and solve for x

0 = 3(10)^x  - 1      add 1 to both sides

1 = 3(10)^x             divide both sides by 3

1/3  = 10^x           take the log of both sides

log (1/3)  = log(10)^x       and we can write

log(1/3) = x log(10)         log(10) =  1   so we can ignore this

log(1/3)  = x  = about  -0.48

The horizontal asymptote   is   y = -1

This is a growth curve because as x grows larger, y grows larger

595 = 230 (1 + r)^8      divide both sides by 230

595/230  = (1 + r)^8     take the 8th root of both sides

1.126 = 1 + r      subtract 1 from both sides

.126  = r  = about 12.6%

.50 + .40m  = .48m     where m is the number of minutes that equalize the cost......subtract .40m  from each side

.50  = .08m     divide both sides by .08

.50 /.08  = m   = 6.25 minutes

The altitude is given by:

sqrt [ 16^2 - 8^2]  = sqrt (256 - 64)  = sqrt [192]  = sqrt [64 * 3]   =  8sqrt(3) m  ≈  13.856 m

14 1/2 =   29/2

12 3/4   = 51/4

So

(29/2)(51/4)   = 1479/8   = 184 7/8

3x+y=19     →  y =  19 - 3x     (1)

2x-6y=-59     (2)

Substituting (1)  into (2), we have

2x - 6 [19 - 3x]  =  -59      simplify

2x - 114 + 18x   = -59       add 114  to both sides

20x  =  55      divide both sides by 20

x = 55/20   = 11/4

And  using (1)     y  =  19 - 3(11/4)  =  [76 - 33] /4  =  43/4