Question

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 1

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)