The half-life of phosphorus-32 is approximately 24.3 days. step 1 of 3 : determine a so that a(t)=a0at describes the amount of phosphorus-32 left after t days, where a0 is the amount at time t=0 . round to six decimal places.

r=-2.8%, The equation is

Step-by-step explanation:

Chemical decay can be represented by the equation . We can find the rate at which it decays by using t=24.3 days and A=0.5 or half the amount at that time. This means in this context.

To solve for r, we will take the natural log of both sides and use log rules to isolate r.

We know so we were able to cancel it out and divide both sides by 24.5.

We solve with a calculator

We change -0.028 into a percent by multiplying by 100 to get -2.8% as the rate.

The equation is

The value of a is a=-0.028524.                                          

Step-by-step explanation:

The function describe the half-life of phosphorus-32 is

Where, is the initial amount.

According to question,

and t=24.3

Substitute in the formula,

Taking ln both side,

Therefore, The value of a is a=-0.028524.

b. 13

step-by-step explanation:

as there are 13 students in bowling class therefore the most reasonable answer is b as only 13 students are in the bowling class.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,