A bug population grows exponentially. It starts with 10 bugs and has 50 an hour later. How many does it have after the start? (No calculator allowed)

Question

A bug population grows exponentially. It starts with 10 bugs and has 50 an hour later. How many does it have after the start?

(No calculator allowed)

A. 10e^(3ln5)

B. 10e^(5ln2)

C. 10e^(2ln(1/2))

D. 10e^(3ln(1/5))

E. None of these

 

Since I had no idea where to begin I decided to try and simplify the answers:

A. 10e^(3ln5) -> 10x5^3

B. 10e^(5ln2) -> 10x2^5
C. 10e^(2ln(1/2)) -> 10x(1/2)^2
D. 10e^(3ln(1/5)) -> 10x(1/5)^3

 

I don't know how to solve this problem and I appreciate any form of help!

 

Answer 1

Exponential growth law:

 

P(t) = P₀e^kt

 

P₀ = initial population = 10

t = elapsed time in hours

k = ?

 

When t = 1 hour,

 

50 = 10e^k(1) = 10e^k

5 = e^k

k = ln5

 

P(t) = 10e^(ln5)t