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Viefleur [7K]
3 years ago
5

Given the function k(t)=2t−1: a. Evaluate k(2). b. Solve(k)=7.

Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
8 0

Answer:

k(2) = 3

t = 4

Step-by-step explanation:

Given

k(t) = 2t - 1

Solving (1): k(2)

Take t as 2 such that t = 2

This gives

k(2) = 2 * 2 - 1

k(2) = 4 - 1

k(2) = 3

Solving (2): k(t) = 7

Substitute 7 for k(t)

7 = 2t - 1

Add 1 to both sides

7 + 1 = 2t - 1 + 1

2t = 8

Divide both sides by 2

t = \frac{8}{2}

t = 4

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A culture started with 5,000 bacteria. After 2 hours, it grew to 6,500 bacteria. Predict how many bacteria will be present after
lesya [120]
This can be expressed as exponential growth of the form:

f=ir^t, f=final amount, i=initial amount, r=common ratio (rate), t=time

In this case we are given the point (2, 6500) and i=5000 so we can solve for the rate...

6500=5000r^2  divide both sides by 5000

1.3=r^2  take the square root of both sides and note that we know r>0

r=1.3^(1/2) so our equation becomes:

f=5000(1.3)^(1/2)^t  and knowing that (a^b)^c=a^(b*c) we can say:

f=5000(1.3)^(t/2)  so for t=18

f=5000(1.3)^9

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7 0
3 years ago
Select all of the situations that represent a linear relationship between x and y.
Harrizon [31]

Answer:

Linear relationship always produces a straight line and are without exponential.

Lets check all the given options:

1. the total area, in square meters, y, of a square garden if the side length is x meters.

The area of a square is

Here, side is 'x' and area 'y' will be .

This is not linear.

2. the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

The equation forms:

When x = 1

When x = 2

=>

When x = 3

=>

This is a linear relation.

3. the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

The equation forms:

When x = 1

When x = 2

=>

When x = 3

=>

This is also linear.

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

The equation forms:

When x = 1

When x = 2

=>

When y = 3

=>

This is also linear in nature.

Read more on Brainly.com - brainly.com/question/12747906#readmore

6 0
3 years ago
Read 2 more answers
An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. W
IceJOKER [234]
The total cost is given by the equation:
C(t) = 45 + 25(h-1) where h is the number of hours worked.

We can check for each option in turn:

Option A:

Inequality 5 < x ≤ 6 means the hour is between 5 hours (not inclusive) to 6 hours (inclusive)
Let's take the number of hours = 5
C(5) = 45 + (5-1)×25 = 145
Let's take the number of hours = 6
Then substitute into C(6) = 45 + (6-1)×25 = 170
We can't take 145 because the value '5' was not inclusive.


Option B:
The inequality is 6 < x ≤ 7
We take number of hours = 6
C(6) = 25(6-1) + 45 = 170
We take number of hours = 7
Then C(7) = 25(7-1) + 45 = 195

Option C:
The inequality is 5 < x ≤ 6
Take the number of hours = 5
C(5) = 25(5-1) + 45 = 145
Take the number of hours = 6
C(6) = 25(6-1) + 45 = 170
We can't take the value 145 as '5' was not inclusive in the range, but we can take 170

Option D:
6 < x ≤ 7
25(6-1) + 45 < C(t) ≤ 25(7-1) + 45
170 < C(t) ≤ 195

Correct answer: C


7 0
3 years ago
Frank started out in his car travelling 45 mph. When Frank was 1/3 miles away, Daniel started out from the same point at 50 mph
Anna007 [38]

Time taken by Daniel to catch up with Frank is 4 minutes.

Step-by-step explanation:

The question is on relative speed; speed of a moving object with respect to another.

The two cars are travelling in the same direction at different speeds thus;

Relative speed = speed of Daniel - speed of Frank = 50-45= 5 mph

The time which the two meet = distance/ relative speed

Distance = 1/3 miles, which equals 0.33 miles

Time taken by Daniel to catch up with Frank is = 0.33/5 =0.066 hours = 4 minutes.

Learn More

Relative speed: brainly.com/question/10681729

Keywords: car, travelling, miles,started at the same point,catch up with

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6 0
3 years ago
Read 2 more answers
Please! I'm being timed!
Kipish [7]
A should be the correct answer. Let me know if I’m right!
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