1. ## Exponential Functions

1)An xray beam of intensity, I0, in passing through absorbing material x millimeters thick merges with an intensity, I, given by I = I0e^-kx. when the material is 9 millimeters thick 50% of the intensity lost.(I0 = initial amount)

a) calculate the value of the constant k to the three decimal places.
b) What percentage intensity, to one decimal place, remains if the material is 20 millimeters thick?

2) A lab technician placed a baterial cell intovial at 5 a.m. the cells divide in such a way that the number of ells doubles every 4 minutes. the vial is full one hour later.
a) how long does it take for the cells to divide to 4096?
b)at what time is the vial half full?
c) at what time is the vial full?

3)Determine the pH, tothe nearest tenth, of an acidic solution whose [OH-] concentration is 3.98x10^-10 mol/L if [H+][OH-]=1.0 x 10^-14. If the ph of a solution is defined as pH=-log(h+)?

MANY THANKS

2. 1a). use, $\displaystyle \frac{I}{I_0}=e^{-9k}$

$\displaystyle \frac{50}{100}=e^{-9k}$

$\displaystyle \frac{1}{2}=e^{-9k}$

solve for k.

1b). Put the value of k in the equation

$\displaystyle \frac{I}{I_0}=e^{-20k}$

and solve for $\displaystyle \frac{I}{I_0}$

2). initial number of cells $\displaystyle A_0 = 1$

final number of cells $\displaystyle A_n=4096$

doubling time d = 4 min

total time, t = ?

a) use, $\displaystyle A_n = A_0 \left(2 \right)^{\frac{t}{d}}$

$\displaystyle 4096= 1\left(2 \right)^{\frac{t}{4}}$

$\displaystyle 2^{12}= \left(2 \right)^{\frac{t}{4}}$

$\displaystyle 12=\frac{t}{4}$

t = 48 min

b) number of bacteria after t = 1 hour = 60 min (when vial is full)

$\displaystyle A_n = A_0 \left(2 \right)^{\frac{t}{d}}$

$\displaystyle A_n = 1 \left(2 \right)^{\frac{60}{4}}$

$\displaystyle A_n = \left(2 \right)^{15}$

$\displaystyle A_n = 32768$

number of bacteria when vial is full = 32768.

number of bacteria when vial is half-full $\displaystyle A_n= \frac{32768}{2} = 16384$

time t = ?

$\displaystyle A_n = A_0\left(2 \right)^{\frac{t}{d}}$

$\displaystyle 16384 = 1\left(2 \right)^{\frac{t}{4}}$

$\displaystyle 2^{14} = \left(2 \right)^{\frac{t}{4}}$

t = 56 min

the vial is half full after 5:56 am

c) the vial is full after one hour, i e, at 6:00 am

3. Thx..
i still need help with 2 b c and 3 =(

4. Originally Posted by T3chnoBoi
Thx..
i still need help with 2 b c and 3 =(
which part you did not get in 2 b c ??

5. at waht time is the vial half full....