All categories

3 years ago

Select Exponential growth or Exponential decay for each function.

Mathematics

1 answer:

Lena [83]3 years ago

7 0

Answer:

f(x)=(1.023) ⋅ 3^x Growth

f(x)=3 ⋅ (0.072)^x Decay

f(x)=4 ⋅ (0.035)^x Decay

f(x)=2 ⋅ (1.34)^x Growth

Step-by-step explanation:

An exponential function at its heart has a base number of rate. If the rate is less than 1, then the function decays. If the base number or rate is greater than 1, then the function grows and increase.

f(x)=(1.023) ⋅ 3^x Rate 3 - Growth

f(x)=3 ⋅ (0.072)^x Rate 0.072 - Decay

f(x)=4 ⋅ (0.035)^x Rate 0.035 - Decay

f(x)=2 ⋅ (1.34)^x Rate 1.34 - Growth

You might be interested in

What is 18 percent of 28 dollars

bixtya [17]

If something costs $28 and is on sale for 18% off, then how much would it cost?

5.04 U.S. dollars

6 0

2 years ago

Read 2 more answers

A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

2 years ago

Is 3x = 2y a linear equation?

mel-nik [20]

Answer:

yes

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Can someone help me with these?

Jet001 [13]

48 is the correct answer because your going to only do the square

4 0

3 years ago

Read 2 more answers

Find the area. Help me please!

Jobisdone [24]

Answer:

16 cm^2

Step-by-step explanation:

Formula = 1/2 * base * height

1/2 * 8 * 4 = 16

16 cm^2

5 0

2 years ago