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3 years ago

3^3x+1= 81 Solve the exponential function

Mathematics

1 answer:

Reil [10]3 years ago

8 0

Answer:

x=1

Step-by-step explanation:

3^ (3x+1) = 81

Rewrite 81 as a power of 3

3^4

3^ (3x+1) = 3^4

Since the bases are the same, the powers are the same

3x+1 =4

Subtract 1 from each side

3x+1-1 =4-1

3x=3

Divide by 3

3x/3 = 3/3

x =1

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A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

$y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48$

The rumor reaches 80% at 8.48 days.

8 0

3 years ago

18. A container of rainwater is evaporating at 1.6

Licemer1 [7]

The answer you are looking for is C

6 0

3 years ago

Read 2 more answers

Solve the inequality and graph its solution...<br> 3+v≤-9

xxTIMURxx [149]

Answer:

v≤-12, and the graph is left 12

Step-by-step explanation:

6 0

2 years ago

PLZ HELP!!!!!! I THINK ITS TRUE BUT IM NOT SURE

suter [353]

Yes it is true! it is true because two different numbers go to the same number, if it was false it would have to be the one number to two different numbers.

Hope that made sense!

5 0

3 years ago

Two mathematical questions attached below.

BartSMP [9]

Answer:

See below

Step-by-step explanation:

$9.( {m}^{3} {n}^{5} )^{ \frac{1}{4} } \\ = m^{\frac{3}{4}}n^{\frac{5}{4}}\\ \\ 10. \sqrt[5]{ \sqrt[4]{x} } \\ = \sqrt[5]{ {x}^{ \frac{1}{4} } } \\ = {( {x}^{ \frac{1}{4} } )}^{ \frac{1}{5} } \\ = {x}^{ \frac{1}{4} \times \frac{1}{5} } \\ = {x}^{ \frac{1}{20} } \\ \\ \sqrt[5]{ \sqrt[3]{ {a}^{2} } } \\ = \sqrt[5]{ {a}^{ \frac{2}{3} } } \\ = {( {a}^{ \frac{2}{3} } )}^{ \frac{1}{5} } \\ = {a}^{ \frac{2}{3} \times \frac{1}{5} } \\ = {a}^{ \frac{2}{15} }$

4 0

2 years ago