What logarithmic function represents the data in the table? x f(x) 1 0 3 1 9 2

Mathematics

2 answers:

kondor19780726 [428]3 years ago

8 0

Answer:

f(x) = log3(x)

Step-by-step explanation:

y = log3(x)

log3: log with base 3

UkoKoshka [18]3 years ago

6 0

Assuming the following columns: (1,0), (3,1), (9,2), then we have:

f(x)=log_a(x), where log_a means logarithm in base a.

x=1, log_a(1)=0 (ok)

x=3, log_a(3)=1, a¹=3, so the base in 3

f(x)=log_3(x)

x=9, log_3(9)=log_3(3²)=2 (ok)

Answer: f(x)=log_3(x)

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(10 POINTS ON THIS) Anika is hiking on a rectangular trail at the national park.There are four resting spots along the corners o

nasty-shy [4]

Answer: 10 miles

Explanation:

We define the following resting spots

A = resting spot whose coordinate is (2,2)
B = resting spot whose coordinate is (2,4)
C = resting spot whose coordinate is (5,2)
D = resting spot whose coordinate is (5,4)

If you plot A, B, C, D, you will notice that

(Perimeter of the trail) = 2[(distance from A to C) + (distance from A to B)]

Note that A and C have the same y-coordinates (second number in their ordered pairs), so the distance from A to C is computed as the difference of their x-coordinates (first number in their ordered pairs). Thus,

(distance from A to C) = 5 - 2 = 3

Moreover, A and B have the same x-coordinates and so we compute the distance from A to B as the difference of their y-coordinates. Then,

(distance from A to B) = 4 - 2 = 2

Hence,

(Perimeter of the trail) = 2[(distance from A to C) + (distance from A to B)]
= 2[2 + 3]
= 2(5)
(Perimeter of the trail) = 10 miles