A bacterium in a petri dish multiplies by a factor of 31 every day. On day O,
1 answer:
Answer:
Step-by-step explanation:
Given that,
The bacterial increase a factor of 31 every day ,
Day 0 = 1 bacterium = 31^0
Day 1 = 31 bacterial = 31¹
Day 2 = 31× 31 bacterial = 31²
Day 3 = 31 × 31 × 31 bacterial = 31³
And so on,
Then, nth day will have
Day n = 31ⁿ bacterial
So, when will the bacterial be 1,000,000,000
Then,
31ⁿ = 1,000,000,000
Take the Natural logarithmic to base 31 of both sides
Log_31 (31)ⁿ = Log_31 (1,000,000,000)
n•Log_31 (31) = Log_31 (1,000,000,000)
Then, log_a (a) = 1
n = Log_31 (1,000,000,000)
Check attachment for better view
Then,
The correct answer is A
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Answer: the distance of the boat from the foot of the lighthouse is 290.5 feet.
Step-by-step explanation:
The right angle triangle ABC representing the scenario is shown in the attached photo.
Angle A is alternate to the angle of depression, hence, they are the same.
The height of the lighthouse represents the opposite side of the right angle triangle. The distance, x of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.
To determine x, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 11.1 = 57/x
x = 57/Tan 11.1 = 57/0.1962
x = 290.5 feet to the nearest tenth.
