Amass of 100 grams of a particular radioactive substance decays according to the function m(t)=100e−t850

, where t> 0 measures time in years.

when does the mass reach 30 grams?

After 1023.4 years the mass of the substance will be 30 g.

Explanation:

Hi there!

Let´s write the function (according to what I found on the web):

We have to find the time "t1" at which the mass of the substance is 30 g. Mathematically:

m(t1) = 30

Then:

Let´s solve the equation for t1. First, divide by 100 both sides of the equation:

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Apply ln to both sides of the equation:

Use the logarithm property: ln (aᵇ) = b ln(a)

ln(0.3) = -t/850 · ln (e)             (ln (e) = 1)

ln(0.3) = -t/850

850 ln(0.3) = -t

t = -850 ln(0.3)

t = 1023.4

After 1023.4 years the mass of the substance will be 30 g.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

number of electrons for neutral cl