Answer:
[tex]\large \boxed{\text{25.66 wk}}[/tex]
Step-by-step explanation:
An exponential function with base b is defined by ƒ(x) = a(b)ˣ.
If b > 1, we have exponential growth.
The formula for your function is garbled, so I shall assume it is
N(t) = 300(1.47)^{t/9}
If the initial population is 300, the new population is 3 × 300.
[tex]\begin{array}{rcl}3 \times 300 & = & 300\cdot(1.47) ^{t/9}\\3 & = & (1.47) ^{t/9}\\\ln3 & = & (t/9)\times\ln1.47\\\dfrac{\ln3 }{\ln1.47} & = & \dfrac{t}{9}\\\\\dfrac{t}{9}& = & 2.8516\\\\t & = & 9\times 2.8516\\ & = & \textbf{25.66 wk}\\\end{array}\\\text{The number of locusts is tripled every $\large \boxed{\textbf{25.66 wk}}$}[/tex]
From the increased population of the locust, the number of locusts is tripled every 0.5 weeks.
From the model function, the rate of change in the locust population is calculated as follows;
N(t) = 300 . 9^t
Table 1
t N(t) = 300 . 9^t
0 300 x 9⁰ = 300
1 300 x 9¹ = 2700
2 300 x 9² = 24300
3 3 00 x 9³ = 218700
The population, got trippled;
300 x 9^t = 300 x 3
9^t = 3
[tex]3^2^t = 3^1\\\\2t = 1\\\\t = 1/2\\\\t = 0.5[/tex]
Thus, from the increased population of the locust, the number of locusts is tripled every 0.5 weeks.
Learn more about rate of change of population here: https://brainly.com/question/16992857
