Jim spins a spinner with colors red, blue, yellow, purple, green, and orange. jim also flips a coin. what is the probability that jim spins a primary color (red, blue, yellow) and flips a head? a) 1 2 b) 1 3 c) 1 4 d) 1 6

Probability=number of specific outcomes/total possible outcomes

And the probability of two events happening at the same time is P(1)*P(2), or the product of the probabilities of each event...

In this case:

P(primary color)=3/6=1/2

P(head)=1/2

P(primary and head)=(1/2)(1/2)=1/4

A.
it is grouth because the exponent is positive
the vertical assemtote is y=0

b.
1 hour: 100e^(0.592(1))=100e^(0.592)≈180.76 bacteria
5 hours: 100e^(0.592(5))≈1929.80 bacteria
10 hours: 100e^(0.592(10))≈37241.17 bacteria
24 hours: 100e^(0.592(24))≈148066223.24 bacteria

c. solve for t
I will solve using both ln and log₁₀ in case your teacher wants one or the other

so
log₁₀ first
B=100e^(0.592t)
divide both sides by 100
B/100=e^(0.592t)
take log₁₀ both sides
log₁₀(B/100)=log₁₀(e^0.592t)
log₁₀(B/100)=0.0592tlog₁₀(e)
divide both sides by 0.592log₁₀(e)


now using ln
B=100e^(0.592t)
divide by 100 both sides
B/100=e^(0.592t)
take ln of both sides
ln(B/100)=0.592tln(e)
ln(B/100)=0.592t
divide both sides by 0.592
(ln(B/100))/0.592=t

d.
using our equation (I'll use ln)
(ln(B/100))/0.592=t
(ln(3500/100))/0.592=t
(ln(35))/0.592=t
6.00566=t
so about 6 hours