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3 years ago

Tell if each equation represents exponential growth, exponential decay or neither.

Mathematics

1 answer:

scoray [572]3 years ago

3 0

Answer:

Exponential growth A, B;

exponential decay C, E;

neither D.

Step-by-step explanation:

The function $y=a\cdot b^x$

represents exponential growth when $b>1;$
represents exponential decay when $0$

A. The equation $f(t)=\dfrac{2}{3}\cdot \left(\dfrac{7}{3}\right)^t$ represents exponential growth, because $\dfrac{7}{3}>1.$

B. The equation $P=22\cdot \left(1.76\right)^x$ represents exponential growth, because $1.76>1.$

C. The equation $V=\dfrac{1}{3}\cdot \left(0.45\right)^x$ represents exponential decay, because $0$

D. The equation $W=3.2\cdot (x)$ represents neither exponential growth nor exponential decay, because this function is linear.

E. The equation $g(x)=4.2\cdot \left(\dfrac{1}{3}\right)^x$ represents exponential decay, because $0$

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A sample of bacteria is decaying according to a half-life model. If the sample begins with 800 bacteria, and after 13 minutes th

nikklg [1K]

Answer:

56.42 minutes

Step-by-step explanation:

The initial sample= y0 = 800

After 13 minutes , amount = 320

Y= y0e-kt

320 = 800e-k(13)

320/800 = e-k13

0.4 = e-k13

In0.4 = -k13

-0.91629= -k13

0.07048= k

Y = 800e-0.07048t

Minutes when the bacterial present will be 15

15 = 800e-0.07048t

15/800= e-0.07048t

0.01875 = e-0.07048t

In 0.01875 = -0.07048t

-3.97656 = -0.07048t

-3.97656/-0.07048= t

56.42 = t

56.42 minutes

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3 years ago

Where is m and p I don't know because it's confusing

Natasha_Volkova [10]

M is 1.75 and P is 2.5

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3 years ago

Read 2 more answers

What’s are the steps to solve 52.2x2.3

forsale [732]

Line up the decimal points and multiply the rest like you would normally do it but drop down the decimal at the end

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3 years ago

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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago

The distance between Dania and Hollywood is shown on the map. What is the actual distance between Dania and Hollywood?

pishuonlain [190]

Answer:

15 miles

Step-by-step explanation:

If there are 2.5 inches and 1 inch is 6 miles, then just multiply 6 by 2.5 to get 15

6*2.5=15

8 0

3 years ago