Question

The estimated number of organisms in a population after t days is shown in the table below. t days estimated number of organisms, n 2 860 4 1,250 6 1,800 8 2,600 10 3,720 Which equation best models the situation?

Answer 1

Answer:

The function $n=591.68(1.2056)^t$ best models the situation.

Step-by-step explanation:

The values in the table do not lie over a straight line because their slope is not a constant; for example

$m_1=\frac{1250=860}{4-2} =195$

$m_2=\frac{1850-1250}{2}=275$

we see here that $m_1\neq m_2$ therefore a linear equation cannot represent this situation.

The values in the table are increasing exponentially , therefore the equation modeling the situation will be of the form:

$n=ab^t$

we take two points from the table for evaluating $a$ and $b$ namely points $(2,860)$ and $(4,1250)$

thus we have

(1). $860=ab^2$

(2).$1250=ab^4$

From equation (1) we solve for $a:$

$a=\frac{860}{b^2}$

and put this value into equation (2)

$1250 =\frac{860}{b^2}b^4$

$b^2=\frac{1250}{860}$

$\boxed{b=1.2056}$

with this value $b$ , we solve for $a$ in equation (1):

$860=a(1.2056)^2$

$a=\frac{860}{(1.2056)^2}$

$\boxed{a=591.68}$

Thus we have the equation

$\boxed{n=591.68(1.2056)^t}$

Answer 2

Answer:

B on Edg2020

Step-by-step explanation: