Step 1: 0.416 = 416⁄1000
Step 2: Simplify 416⁄1000 = 52⁄125
Answer:
27.76 grams will be present in 500 years
Step-by-step explanation:
The given formula is 
, where A is the value of the substance in t years, and 
is the initial value
∵ The half-life is a substance is 375 years
- Substitute A by 
and t by 375 to find the value of k
∴ 
- Divide both sides by
∴ 
- Insert ㏑ in both sides
∴ ㏑( 
) = ㏑ ( 
)
- Remember ㏑ ( 
) = n
∵ ㏑ ( ) = 375 k
∴ ㏑( ) = 375 k
- Divide both sides by 375
∴ k ≈ -0.00185
∴ 
∵ 70 grams is present now
- That means the initial value is 70 grams
∴ = 70
∵ The time is 500 years
∴ t = 500
- Substitute the values of and t in the formula
∵ 
∴ A = 27.76
∴ 27.76 grams will be present in 500 years
At least $73.50 for 7x3 is 21 gallons and 10.50x7 is $73.50
Answer:
f'(x) = 5 x<4
= 2x 4<x<6
= 4 x>6
Domain is all real numbers except 4 and 6
Step-by-step explanation:
We need to find the derivative of the piecewise function
f'(x) = 5 x<4
= 2x 4≤x≤6
= 4 x>6
Is the function continuous at 4
f(4-) = 5(4) - 6 = 20-6 = 14
f(4+) = 4^2 -2 = 16-2 = 14
this is continuous, so there is no problem with the continuity here
Is the function continuous at
f(6-) = 6^2 -2 = 36-2 = 34
f(6+) = 4(6)+10 = 24+10 = 34
this is continuous, so there is no problem with the continuity here
Now we need to check the derivatives
f'(4-) = 5
f'(4+) = 8
This is not continuous, so we get a piecewise definition for the derivative excluding 4
f'(6-) =12
f'(6+) =4
This is not continuous, so we get a piecewise definition for the derivative excluding 6
12.79 + .64 = 13.43
20 - 13.43 = $6.57
Hopes this helps :)
