Question

The exponential function that models cell duplication in a lab is f(t) = 2^ t+2 where f(t) is the number of cells after time t (in hours). After how many hours has the number of cells increased to 10,000?

Answer 1

Answer:

12.29

Step-by-step explanation:

Answer 2

ANSWER

$11.29 \: hours$

EXPLANATION

The exponential function that models cell duplication in the lab is given as

$f(t) = {2}^{t + 2}$

We want to determine the time it will take for the cells to increase to
$10,000.$

In other words, we want to find the value of
$t$
when
$f(t) = 10,000$

This gives us the equation,

$10,000 = {2}^{t + 2}$

Recall that,

${a}^{m + n} = {a}^{m} \times {a}^{n}$

We apply this property to the right hand side to obtain,

$10,000 = {2}^{t} \times {2}^{2}$

This implies that,

$10,000 =4 \times {2}^{t}$

We divide both sides by 4 to get,

$2500 = {2}^{t}$

We take the antilogarithm of both sides to base 10 to get,

$t = log_{2}(2500)$

This implies that,

$t = 11.29 \: hours$
to the nearest hundredth.