222k views
0 votes
1. )The function f(x)=12,500(0.87)^x models the value of a car x years after it is purchased.

How does the average rate of change between years 11 and 15 compare to the average rate of change between years 1 and 5?

A. The average rate of change between years 11 and 15 is about 2 times the rate between years 1 and 5.

B. The average rate of change between years 11 and 15 is about 3 times the rate between years 1 and 5.

C. The average rate of change between years 11 and 15 is about 13 the rate between years 1 and 5.

D. The average rate of change between years 11 and 15 is about 14 the rate between years 1 and 5.

2. A population of beavers decreases exponentially at a rate of 7.5% per year.

What is the equivalent monthly rate to the nearest hundredth of a percent?


A. 0.65%

B. 0.81%

C. 0.91%

D. 2.37%

User Daveman
by
8.1k points

2 Answers

5 votes

Answer:

The correct answer is A. The average rate of change between years 11 and 15 is about 2 times the rate between years 1 and 5.

Explanation:

User Dreamzor
by
8.3k points
3 votes
1] Given that the value of x has been modeled by f(x)=12500(0.87)^x, then:
the rate of change between years 1 and 5 will be:
rate of change is given by:
[f(b)-f(a)]/(b-a)
thus:
f(1)=12500(0.87)^1=10875
f(5)=12500(0.87)^5=6230.3
rate of change will be:
(6230.3-10875)/(5-1)
=-1161.2
rate of change in years 11 to 15 will be:
f(11)=12500(0.87)^11=2701.6
f(15)=12500(0.87)^15=1,547.74
thus the rate of change will be:
(1547.74-2701.6)/(15-11)
=-288
dividing the two rates of change we get:
-288/-1161.2
-=1/4
comparing the two rate of change we conclude that:
The average rate of change between years 11 and 15 is about 1/4 the rate between years 1 and 5.
The answer is D]
2] Given that the population of beavers decreases exponentially at the rate of 7.5% per year, the monthly rate will be:
monthly rate=(n/12)
where n is the number of months
=7.5/12
=0.625
This is approximately equal to 0.65%. The correct answer is A. 0.65%

User Michael Powell
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories