Question

A certain strain of bacteria is growing at a rate of 44% per hour, and with 2,000 bacteria initially, this event can be modeled by the equation B(t) = 2,000(1.44)t. With this fast growth rate, scientists want to know what the equivalent growth rate is per minute. Using rational exponents, what is an equivalent expression for this bacterial growth, expressed as a growth rate per minute?

Answer 1

The given equation for the growth rate per hour is:

$B(t)=2,000(1.44)^t$

Where t is the time in hours.

The equivalent growth rate per minute would be the equivalent in minutes for hours, then:

$1\min \cdot\frac{t\text{ hours}}{60\min }=\frac{t}{60}$

Where t is the time in minutes, then the answer is:

$B(t)=2,000(1.44)^{\frac{t}{60}}$