If the function Q(t)=4e-0.00938t models the quantity (in kg) of an element in a storage unit after t years, how long will it be before the quantity is less than 1.5kg? Round to the nearest year.

105 years

Step-by-step explanation:

Given the function :

Q(t) = 4e^(-0.00938t)

Q = Quantity in kilogram of an element in a storage unit after t years

how long will it be before the quantity is less than 1.5kg

Inputting Q = 1.5kg into the equation:

1.5 = 4e^(-0.00938t)

Divide both sides by 4

(1.5 / 4) = (4e^(-0.00938t) / 4)

0.375 = e^(-0.00938t)

Take the ln of both sides

In(0.375) = In(e^(-0.00938t))

−0.980829 = -0.00938t

Divide both sides by 0.00938

0.00938t / 0.00938 = 0.980829 /0.00938

t = 104.56599

When t = 104.56599 years , the quantity in kilogram of the element in storage will be exactly 1.5kg

Therefore, when t = 105 years, the quantity of element in storage will be less than 1.5kg

this was already solved by me with a different person. if you look it up in the search bar at the top of the page, you will get the answer.

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.