Question

Nuno set up a series of dominoes. he starts by knocking over 10 dominoes. every second after that, the number of dominoes that are knocked over doubles. there are 2,560 dominoes in the chain. if the dominoes continue to fall at this rate, how long will it take until all of the dominoes fall over? choose the equation for the number of dominoes that fall over, d, in terms of the number of seconds since the chain reaction started, s, and the correct solution.

Answer 1

It will take 8 seconds for all of the dominoes to fall over.

This will be an exponential function.  To find the growth rate, we can write out the terms of the sequence that goes along with it:  10, 20, 40, ...

"Growth rate" is the same as percent of increase or decrease.  We find the amount of increase and divide by the original amount:  20-10 = 10 increase; 10/10 = 1.

The exponential function is of the form
f(x) = a*(1+r)ˣ, where a is the initial value (10), r is the growth rate (1), and x is the number of time periods.  Using the variables given to us in the problem along with this information, we have:

$d(s)=10(1+1)^s \\ \\2560=10(2)^s$

Divide both sides by 10:
$\frac{2560}{10}=\frac{10(2)^s}{10} \\ \\256=2^s$

We will use logarithms to solve this:
$\log_2 256=s \\8=s$

Answer 2

Answer:

10 • 2s = D

8 seconds

Step-by-step explanation: