Respuesta :
Answer:
b. 2005
Step-by-step explanation:
(apex)
300=150(1.07)^x
1.07^x=2
x=ln 2/ln 1.07
=10.24
1995 plus ten years = 2005
hope this helps
Answer:
B. 2005
Step-by-step explanation:
We have been given that population of deer in a certain national park can be approximated by the function [tex]P(x)=150(1.07)^x[/tex], where x is the number of years since 1995. We are asked to find the year in which population will reach 300.
To solve our given problem, we will equate [tex]P(x)=300[/tex] and solve for x as:
[tex]300=150(1.07)^x[/tex]
[tex]\frac{300}{150}=\frac{150(1.07)^x}{150}[/tex]
[tex]2=(1.07)^x[/tex]
Now, we will take natural log on both sides as:
[tex]\text{ln}(2)=\text{ln}((1.07)^x)[/tex]
[tex]\text{ln}(2)=x\text{ln}(1.07)[/tex]
[tex]x=\frac{\text{ln}(2)}{\text{ln}(1.07)}[/tex]
[tex]x=10.2447[/tex]
[tex]x\approx 10[/tex]
Now, we will find 10 years after 1995 that is [tex]1995+10=2005[/tex].
Therefore, the population will be 300 in year 2005 and option B is the correct choice.
