Question

A certain culture initially contains 10,000 bacteria and increase by 20% after every hour.
A) What will be the formula for numbers N(t) of bacteria after "t" hours?
B) How many bacteria are in culture at the end of 10 hours?

Answer 1

Every hour, the amount is increased by 20%, meaning it's multiplied by 1.2

So,

N(t) = N(initial)*((1.2)^t)
= 10000*((1.2)^t)
So every hour the number gets multiplied with an additional 1.2


When t = 10,

N(10) = 10000*((1.2)^10)
= 10000*6.191
= 61,910

Answer 2

Exponential Growth:

N(t) = N ∙ ( 1 + r )ᵗ

N = initial amount

r = growth rate

t = time elapsed

In this case:

N = 10,000

r = 20% = 20 / 100 = 0.2


A)

N(t) = 10,000 ∙ ( 1 + 0.2 )ᵗ

N(t) = 10,000 ∙ 1.2 ᵗ


B)

N(10) = 10,000 ∙ 1.2 ¹⁰ = 10,000 ∙ 1.2 ¹⁰ = 10,000 ∙ 6.1917364224 = 61,917.364224

Approx.

62,000