Question

During a bean flipping experiment Fiona modeled her data using the function

Answer 1

Answer:

C.5

Step-by-step explanation:

Fiona:

After t trials, she would have:

$f(t) = 4.127(1.468)^t$

Karl:

After t trials, he would have:

$k(t) = 0.897(1.992)^t$

At what number of trials would Fiona and Karl have the same number of beans?

This is t for which:

$f(t) = k(t)$

So

$4.127(1.468)^t = 0.897(1.992)^t$

$0.897(1.992)^t = 4.127(1.468)^t$

$\frac{(1.992)^t}{(1.468)^t} = \frac{4.127}{0.897}$

$(\frac{1.992}{1.468})^t = 4.6$

$(1.35695)^t = 4.6$

$\log{(1.35695)^t} = \log{4.6}$

$t\log{1.35695} = \log{4.6}$

$t = \frac{\log{4.6}}{\log{1.35695}}$

$t = 5$

So the correct answer is 5 trials, option C.