On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom.
The relationship between the elapsed time, tt, in weeks, since the beginning of spring, and the total number of locusts, N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function:
N(t)=300⋅9t
Answers
Given : On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom.
N(t) = 300 . 9^t
To Find : rate of change in the locust population.
The number of locusts is tripled every ---- weeks.
Solution:
t N(t) = 300 . 9^t
0 300 * 9⁰ = 300
1 300 * 9¹ = 2700
2 300 * 9² = 24300
3 300 * 9³ = 218700
Becomes 9 times every Week
increase by 8 time every week
Rate of change = (300 . 9^(t+ 1) - 300 . 9^t )/(t + 1 - t)
= 9.300 . 9^t - 300 . 9^t
= 300 . 9^t(8)
= 8 times of previous week.
initially 300
Got tripled = 300 * 3
300 . 9^t = 300 * 3
=> 9^t = 3
=> t = 1/2
After 1/2 week
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