Exponential Growth

Question

Please help me understand by showing me how to set up the problem with correct formula.

 

An infectious strain of bacteria increases in number at a relative growth rate of 240 percent per hour. When a certain critical number of bacteria are present in the bloodstream, a person becomes ill. If a single bacterium infects a person, the critical level is reached in 24 hours. How long will it take for the critical level to be reached if the same person is infected with 10 bacteria?

Answer 1

A = a₀(2.4)^h

A = 1(2.4)²⁴

(2.4)²⁴ = 10(2.4)^h

(2.4)²⁴ / 10 = (2.4)^h

24 ln 2.4 - ln 10 = h ln 2.4

24(0.875) - 2.303 = h (0.875)

21.34 = h