Question

Write an equation in the form y = a(b)^x that represents the growth of a bacteria colony at noon. It starts with 180 bacteria and increases at a rate of 22% per hour.

Answer 1

The equation for the exponential growth of a bacterial colony starting with 180 bacteria and increasing at a rate of 22% per hour is y = 180(1.22)^x, with x representing time in hours.

Step-by-step explanation:

To write an equation in the form y = a(b)^x that represents the exponential growth of a bacteria colony that increases at a rate of 22% per hour, starting with 180 bacteria, we need to identify the initial amount a as the starting number of bacteria and b as the growth factor per hour.

Since the colony starts with 180 bacteria, a is 180. The growth rate of 22% per hour can be converted to a growth factor of 1 + 0.22 = 1.22. So, b will be 1.22.

The equation representing the bacterial growth is therefore y = 180(1.22)^x, where x is the time in hours since the start at noon.