SOLUTION: I need help with this word problem: The radioactive bismuth isotope (210 Bi)disinigrates according to q=k(2)^(-t/5) where k is constant and t is the time in days. Express t in t

Question 116789This question is from textbook Fund of Algo and trig
: I need help with this word problem:
The radioactive bismuth isotope (210 Bi)disinigrates according to q=k(2)^(-t/5) where k is constant and t is the time in days. Express t in terms of Q and k.
Can anyone solve or set up this problem?
thanks This question is from textbook Fund of Algo and trig

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This is one way of working the problem.
.
Given:
.

.
Begin by dividing both sides of this equation by k to get:
.

.
Take the logarithm of both sides. I chose to use base 10, but you could just as easily use
base e or any other base you prefer.
.

.
By the rules of logarithms, the exponent on the right side can be brought out as a multiplier
of the logarithm to give:
.

.
Divide both sides by and you get:
.

.
Multiply both sides of this equation by -5 to solve for t and you have:
.

.
Just to get it into a little more standard form, transpose the equation (switch sides) and
you have:
.

.
You can simplify this a little further by recognizing that is just a
number. A calculator will tell you that it is 0.301028885 and if you like, you can round this
to 0.3010 (Choose the amount of rounding you want.) This makes the equation:
.

.
and if you divide the denominator into the -5 in the numerator, the equation reduces to:
.

.
Might as well round off -16.61129568 to -16.6113 or whatever you want ... to get:
.

.
You could stop here or you could use the rule that
and substitute into the equation for t to get:
.

.
Note that you can expect that must be bigger than to prevent
you from getting a negative answer for t.
.
Check the above for errors. The basic process of using the logarithm is one that can be used
to solve this problem, though.
.
Hope this helps you to get on with the problem.
.
RELATED QUESTIONS
Could someone please help me with this problem? Use the formula N = Ie^kt, where N is the (answered by stanbon)

Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of (answered by ikleyn,math_tutor2020)

Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of (answered by ankor@dixie-net.com)

Hello I really need help with this word problem a radioactive isotope decays... (answered by josgarithmetic)

I'm having a hard time with exponential functions. Here's the problem: The radioactive (answered by Boreal)

Use the formula N = Ie^(kt), where N is the number of items in terms of the initial... (answered by Theo)

Use the formula N = Iekt, where N is the number of items in terms of the initial... (answered by stanbon)

Use the formula N = Iekt, where N is the number of items in terms of the initial... (answered by nerdybill)

Solve the problem. Use the formula N = Iekt, where N is the number of items in terms... (answered by ankor@dixie-net.com)