There is a population of 1,000,000 bacteria in a colony. if the number of bacteria doubles every 270 hours, what will the population be in 810 hours from now?

8000000 bacteria

Step-by-step explanation:

We would apply the formula,

y = ab^t

Where

A represents the initial amount of bacteria.

t represents the doubling time.

From the information given

A = 1000000

t = 270 hours

Since after 270 hours, the population doubles, then

y = 2 × 1000000 = 2000000

Therefore

2000000 = 1000000 × b^270

2 = b^270

Raising both sides of the equation by 1/270, it becomes

2^(1/270) = b

The equation becomes

y = 1000000 × 2^(1/270) ×t

y = 1000000 × 2^(t/270)

Therefore, the population in 810 hours hours time would be

y = 1000000 × 2^(810/270)

y = 1000000 × 2^3

y = 8000000 bacteria

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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