1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
iren [92.7K]
3 years ago
5

A linear function and an exponential function are graphed below. Find possible formulas for the functions f(t), in blue, and g(t

), in red, that go through the points (3,18) and (15,6).

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
3 0

Answer:

f(t) = -t + 21

g(t) = 18*e^( - t / 12 + 1/4 )

Step-by-step explanation:

Given:

- The graphs for the similar question is attached.

- The same graph would be used as reference but with different coordinates for point of intersection of f(t) and g(t) @ ( 3 , 18 ) & ( 15 , 6 ).

Find:

- The formulas for functions f(t) and g(t).

Solution:

- First we will determine f(t) the blue graph which is a "linear" function. The general equation for the linear function is given as:

                                    f(t) = m*t + c

Where, m: is the gradient  ( constant )

            c: The f(t) intercept. ( constant )

- The gradient m can be determined by the given points that lie on the graph:

                         m = ( f(t2) - f(t1) ) / ( t2 - t1 )

                         m = ( 6 - 18 ) / ( 15 - 3 )

                         m = -12 / 12 = -1

- The constant c can be evaluated by using any one point and m substituted back into the linear expression as follows:

                          f(t) = -t + c

                          18 = -(3) + c

                           c = 21

- The function f(t) is as follows:

                            f(t) = -t + 21

- The general expression for an exponential function can be written as:

                           g(t) = a*e^(b*t)

Where, a and b are constants to be evaluated.

- We will develop two expressions for g(t) using two given points that lie on the curve as follows:

                           18 = a*e^(3*b)

                           6 = a*e^(15*b)

- Divide the two expressions we have:

                           3 = e^( 3b - 15b )

                           Ln(3) = -12*b

                           b = - Ln(3) / 12

- Then the expression 1 becomes:

                          18 = a*e^( - Ln(3)*3 / 12)

                          18 = 3*a*e^(-1/4)

                           6 = a / e^(0.25)

                           a = 6*e^( 1 / 4 )

- The function g(t) can be expressed as:

                          g(t) = 18*e^( - t / 12 + 1/4 )

You might be interested in
What is the percent of change from 10 to 5?
NNADVOKAT [17]

Answer:

50% decrease

Step-by-step explanation:

\dfrac{(V_2-V_1)}{|V_1|} \times 100

= \dfrac{(5 - 10)}{|10|} \times 100

= \dfrac{-5}{10} \times 100

= -0.5 \times 100

= -50\% \; \text{change}

= 50\% \; \text{decrease}

8 0
3 years ago
Read 2 more answers
A social psychologist conducts an experiment and finds a statistically significant result. This means that the a. experiment is
coldgirl [10]

Considering that the hypothesis test found an statistically significant result, it is found that the correct option is:

c. probability of obtaining this finding by chance alone is less than some quantity.

<h3>What is an hypothesis test?</h3>
  • When a hypothesis test, there are two hypothesis, the null and the alternative hypothesis.
  • There is also a significance level.
  • If the probability of obtaining the finding by chance is less than the significant value, the result is statistically significant.

Hence, according to these bullet points, option C is correct.

You can learn more about hypothesis tests at brainly.com/question/16313918

7 0
3 years ago
If sin theta = -0.7660, which of the following represents an approximate value of tan theta, for 180 degrees &lt; theta &lt; 270
Elis [28]
We have that
sin ∅=-0.7660

the sin ∅ is negative
so 
∅ belong to the III or IV quadrant
but
180°< ∅ < 270°
hence
∅ belong to the III quadrant
sin ∅=-0.7660
sin² ∅+cos² ∅=1
cos² ∅=1-sin² ∅------> cos² ∅=1-(0.7660)²-----> 0.4132
cos ∅=√0.4132-----> cos ∅=0.6428
the value of cos ∅ is negative-------> III quadrant
cos ∅=-0.6428

tan ∅=sin ∅/ cos ∅----> tan ∅=-0.7660/-0.6428----> tan ∅=1.1917

the answer is
tan ∅ is 1.1917
4 0
3 years ago
Which is larger 0.7 or 3/4
Ksenya-84 [330]
3/4 is 0.75.
3/4 is larger than 0.7
3 0
3 years ago
Read 2 more answers
How do you find the area of this figure?
loris [4]

Answer:

seis CM para 10 yd por eso

8 0
2 years ago
Other questions:
  • In relation t a functions? Is the inverse of relation t function
    12·1 answer
  • After t seconds, a ball tossed in the air from the ground level reaches a height of h feet given by the equation h = 144t-16t^2
    13·2 answers
  • what is true about every rotation? the image and pre-image are congruent. the image is larger than the pre-image. the image over
    14·2 answers
  • Someone please help!! i mark brainliest!!​
    11·1 answer
  • If I roll a fair number cube 150 times, how many times should I expect to roll a number less than 4?
    6·1 answer
  • Someone help<br> me plsss
    6·1 answer
  • Find the measure of the indicated angle.
    13·1 answer
  • Find the length of side x in simplest radical form with a rational denominator.
    7·1 answer
  • Solve for x.<br><br> -5x = -10
    15·2 answers
  • Please help with this!!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!