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
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?
2 answers
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
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