29.
![f(x) = -x^2-7x-6](https://img.qammunity.org/2022/formulas/mathematics/high-school/5apivgabi8b6iz26gqfpc8c8r5mhy5c3gd.png)
As
,
.
This can be easily verified by looking at the graph (graph of a quadratic equation).
30.
The growth of a population is not linear, it's exponential.
31.
Exponential growth > polynomial, so
.
35.
![V(t) = 30\cdot (25)^{(t)/(20)}](https://img.qammunity.org/2022/formulas/mathematics/high-school/brbs9yi3hipn4srad9kcrk82xjugntznh8.png)
The question is asking V(t) for t = 40.
![V(40) = 30\cdot (25)^{(40)/(20)} \\~\\V(40) = 30\cdot 25^2 \\~\\V(40) = 30\cdot 625 \\~\\V(40) = 18750](https://img.qammunity.org/2022/formulas/mathematics/high-school/1kyq2cthnrqx54gy9d5rgjhvdo1flze7gl.png)
36.
The point of symmetry of a quadratic equation
is at its vertice:
![V_x = (-b)/(2a)](https://img.qammunity.org/2022/formulas/mathematics/high-school/hl1zvj9l4ni7qj2fn3b5z4r621smxd7md7.png)
![V_x = (6)/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/syz1ujkboknlzly1u435y3ndc2pjr6ls30.png)
![V_x = 3](https://img.qammunity.org/2022/formulas/mathematics/high-school/ga5ony1gzynhcm1vi4jehtp2nvemjnuey1.png)
The line is x= 3.