The number of bacteria in culture grows 80% each hour. Suppose. There are 250 bacteria in the original culture.

a. Write an exponential growth model showing the number of bacteria after x hours.

b. Calculate the number of bacteria after 10 hours.

Answer: (a) y = 250 (1.8) ˣ (b) 89,262 bacteria

Step-by-step explanation:

Use the exponential growth formula y = a (b) ˣ where

a = Initial Value b = 1 + r (for growth) or 1 - r for decay r = rate (convert percent to a decimal)

a) Given: a = 250, r = 80% (.80) → b = 1.8

y = 250 (1.8) ˣ

b) Given: x = 10

y = 250 (1.8) ¹⁰

y = 89,261.68 = 89,262 (rounded to the nearest whole number)