Math, asked by Ruhikaul9, 6 months ago

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

Answered by amitnrw
5

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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