The half-life is a substance is 375 years. If 70 grams is present now, how much will be present in 500 years?

Use the formula pictured

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

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1