As we know

Y (0) = y°

Put t = 0 in

Y (0) = Aekt

Y (0) = A

So A= y°

Exponential Growth Example Solution:

we have y0 = 500

t= 3.5

The number of cells doubles every 3.5 hours, so after 3.5 hours there should be 1000 cells.

Therefore after 12 hours there will be cells in the dish.

HALF LIFE:

Example 1 solution

Example 2 solution

Falling object example

Hence v(0)=0

So

C=0.

Put again in v

So

V= -9.81t

Encryption example

18 5

A = 4 0

18 21

13 0

B = 4 -2

-1 3

67 -21

X = A B = 16 -8

51 27

52 -26

The message that you would pass on to the other person is the stream of numbers 67, -21, 16, -8, 51, 27, 52, -26.

DECRYPTION

67 -21

X = 16 -8

51 27

52 -26

B-1 = 0.3 0.2

0.1 0.4

18 5

A = X B-1 = 4 0

18 21

13 0

The receiver then takes the matrix and breaks it apart into values 18, 5, 4, 0, 18, 21, 13, 0 and converts

each of those into a character according to the numbering scheme. 18=R, 5=E, 4=D, 0=space, 18=R,

21=U, 13=M, 0=space.

Triangle area

Evaluate that determinant. I'll expand on column 1.

-2 2 1

1 5 1 = + (-2) 5 1 - 1 2 1 + 6 2 1

6 -1 1 -1 1 -1 1 5 1

= -2 ( 5 + 1 ) - 1 ( 2 + 1 ) + 6 ( 2 - 5 ) = -2 ( 6 ) - 1 ( 3 ) + 6 ( -3 ) = -12 - 3 - 18 = -33.

It is possible that you will get a negative determinant, like we did here. Don't worry about that. The sign is determined by the order you put the points in and can be easily changed just by switching two rows of the determinant. Area, on the other hand, can't be negative, so if you get a negative, just drop the sign and make it positive. Finally, divide it by 2 to find the area.

| -33 | = 33 33 / 2 = 16.5, which was the area.