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
ale4655 [162]
3 years ago
8

The amount, A, in milligrams, of radioactive material remaining in a container can be modeled by the exponential function A(t) =

5(0.5)0.25t, where t is time, in years. Based on this model, how many years does it take for half of the original radioactive material to be left remaining?
Mathematics
1 answer:
lisov135 [29]3 years ago
4 0

Answer: 4 years


Step-by-step explanation:

A(0) has to be amount at start. Assume that's 5mg

Then A(t) = 5×(0.5)^(0.25t) = 5×2^(-t/4),

(also known as 5 exp(-λ t) with λ = ln(2)/4, incidentally).


We need to such that A(t) = 2.5mg, or 2^(-t/4) is 1/2, which happens when -t/4 is -1, or t is 4.



You might be interested in
PLEASE HELP THE QUESTION IS BELOW!!
irina [24]

Answer:

Step-by-step explanation:

B=3x-2

C=12x+2

D=B=3x-2 (Vertically opposite angles)

A=?

Now; we know, A+B+C+D=360 deg.

=>A=360-(B+C+D)

  =360-(3x-2+12x+2+3x-2)

  =360-(18x-2) ----[1]

B+C=180 deg. (linear pair)

=> 3x-2+12x+2=180

=> 15x=180

=> x=180/15

   =12 ---[2]

subsitute [2] in [1];

=> A= 360-(18x-2)

   = 360-(18*12-2)

   = 360-(116-2)

   = 360-214

   = 146 deg.

   

So, the correct answer is (D).

Hope the answer is useful.  

8 0
3 years ago
Read 2 more answers
What is the measure of <DCF
Shtirlitz [24]
129 degrees you just add DCE and ECF together
5 0
3 years ago
Read 2 more answers
Whats the answer to this please
anastassius [24]
Y = 3x
so
if x = 5 then y = 15
if x = 10 then y = 30

so a = 10 and b = 15

answer is B. second choice
a = 10 and b = 15
3 0
3 years ago
5 time 5 to the power of 2 simplified
Maksim231197 [3]
Im not sure wym but i think the answer is 20
3 0
3 years ago
Read 2 more answers
1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING
iogann1982 [59]

If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

then

y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}

We can solve the recurrence exactly by substitution:

a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0

\implies a_n=\dfrac{(-2)^n}{n!}a_0

So the ODE has solution

y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

which you may recognize as the power series of the exponential function. Then

\boxed{y(x)=a_0e^{-2x}}

7 0
3 years ago
Other questions:
  • If h(x) = -2x – 10, find h(-4).<br> -2<br> -18<br> -3<br> -16
    5·2 answers
  • Gas Mileage is how many miles you travel on one gallon of gasoline. A new Honda Accord Hybrid ( part electric, part gasoline ) t
    13·1 answer
  • a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet
    9·1 answer
  • An experiment is broken up into two parts. In the first part of the experiment a penny is tossed in the air. If the coin lands o
    11·1 answer
  • Find the midpoint of the segment with the following endpoints.<br> (5,9) and (0,3)
    9·2 answers
  • a triangle has a height of 34 inches and an area of 391 square inches. Which equation can be used to find the base of the triang
    8·1 answer
  • Sarah makes 10% commission on houses she sells. She recently sold a house for $159,000. What would be Sarah's commission?
    14·2 answers
  • Which number line shows the solution to the inequality -4x + 3 &lt; -5
    13·1 answer
  • What is the product 7/3×5/12​
    7·2 answers
  • Find the area of the circle with the following dimension​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!