A culture of bacteria has an initial population of 860 bacteria and doubles every 9 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 hours, P_0P 0 ​ is the initial population, is the time in hours and is the doubling time, what is the population of bacteria in the culture after 4 hours, ?

1170

Step-by-step explanation:P_0=860

P

0

​

=860

The initial population

t=4

t=4

Time elapsed

d=9

d=9

The doubling time

P_t = P_0\cdot 2^{\frac{t}{d}}

P

t

​

=P

0

​

⋅2

d

t

​

P_t=860\cdot 2^\frac{4}{9}

P

t

​

=860⋅2

9

4

​

Plug in

P_t=1170.2794\approx1170

P

t

​

=1170.2794≈1170

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

oof

step-by-step explanation: