Answer:
10077
Step-by-step explanation:
A culture of bacteria has an initial population of 5400 bacteria and doubles every 10 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P
t
=P
0
⋅2
d
t
, where P_tP
t
is the population after t hours, P_0P
0
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 9 hours, to the nearest whole number?
P_0=5400
P
0
=5400
The initial population
t=9
t=9
Time elapsed
d=10
d=10
The doubling time
P_t = P_0\cdot 2^{\frac{t}{d}}
P
t
=P
0
⋅2
d
t
P_t=5400\cdot 2^\frac{9}{10}
P
t
=5400⋅2
10
9
Plug in
P_t=10076.7563\approx10077
P
t
=10076.7563≈10077
Use parenthesis in the calculator for the exponent
