Answer:
P(t) = 258( 1 + 6%)^t
Step-by-step explanation:
Given that the population of caribou in a forest grows at a rate of 6% every year. If there are currently 258 caribou, the function representing the number of caribou in the forest in t years will be
P(t) = 258( 1 + 6%)^t
Since it is increasing, it will be 1 + 6%
Where P(t) is the function representing the population after t years.
258 is the current or initial population.
Answer:
<h2>3(cos 336 + i sin 336)</h2>
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336)
Answer:
3x+12
Step-by-step explanation:
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