how many days does a scientist grow a culture of 3000 cells at 7 % growth per day to increase the number of cells by 630 ?

Question

choices are a. 2 days b. 3 days c.8 days d.10 days 

Answer 1

A = A₀e^kt

 

where A₀ = 3000, k = 7% (or 0.07)

 

A = (3000 + 630) = 3630 = 3000e^[(0.07)t]

 

Our goal is to find t

 

[(3630)/(3000)] = e^[(0.07)t]

 

ln{[(3630)/(3000)]} = (0.07)t

 

(0.07)t = 2*ln(11/10)

 

t = = 2.7 days

 

so the correct answer is b.

Answer 2

This is an example of exponential growth. The number of cells after n days can be modeled with the function f(n) = 3000*1.07^n

 

We have

3000*1.07^n = 3630

1.07^n = 1.21

ln(1.07^n) = ln(1.21)

n*ln(1.07) = ln(1.21)

n = ln(1.21)/ln(1.07) ≈ 2.817

 

The correct answer is 3 days.

Answer 3

3000 * 0.07 d = 630

 

  210 d = 630

 

 

   d = 630 = 3 days

          210

 

Answer 4

Taking the problem the way it is and given the answers, 7% of 3000 is 210 cells the first day.

The second day you have 7% of 3210 which is 224.7 for a total of 3434.7 cells.

The third day 7% of 3434.7 is 240.429 for a total of 3675.129 cells.

The answer is 3 days. However, given that you have the answers and 7% of 3000 is 210,

the second day you will have a little more than 210 (224.7) and the third day you will have a little

more than 224.7 (240.429). In 3 days you should have a little more than 3*210=630; and

you do, you have 675.129 cells. 2 days isn't enough time ( a little more than 420),

and 8 days is way too many days because 8*210=1680, way too many cells.

You can look at this as a compound interest problem.

3630=3000(1.07)^n

3630/3000=(1.07)^n

1.21=(1.07)^n

log(1.21)=log(1.07)^n

0.082785=n(0.029383)

0.082785/0.029383=n

2.817 days=n

2.817 is closest to 3 days

 

Completely forgot about exponential growth and decay.  The compound interest formula was the first thing that came to mind.

 

 

Answer 5

 

3630 = 3000 ( 1 + 7/100) ^ n

3630/3000 = 1.07 ^ n

1.21 = 1.07^n

Take log on both sides

log 1.21 = n log 1.07

n = log (1.21)/log(1.07) = 2.8 days = 3 days approximately

:)