Radium 226 has a decay rate that satisfies the differential equation d'(t)= -.00043d(t). assume that d(0)=100.
what is d(t)?
how much is left after 100 years? (round to nearest hundredth.)
to the nearest year, what is the life half life of radium 226?

A)

B)

C) τ=2326 years

Step-by-step explanation:

A)

Consider the differential equation:

Separate variables dD and dt:

Integrate: Remember that The integral of dD/D is ln(D).

And do , so:

B)

The function we have found is a function that let us know how many of Ra is after t years, so, evaluate the function at t=100:

Which rounded is 95.8.

C) For this equation it is known that the life half life τ is equal to (1/λ), where λ is the exponential number that is multiplying to -t in the D(t) function; so for this case, λ=0.00043, and the life half life is ,

which rounded is equal to 2326 years.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

3,750 deer

step-by-step explanation:

1,500 is 15 times larger than 100

lets make 250 15 times larger.

3750 deer