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Answer:
(a)Yes, it is an exponential function.
(b)![P(t)=200\cdot 2^{t/20}](https://tex.z-dn.net/?f=P%28t%29%3D200%5Ccdot%202%5E%7Bt%2F20%7D)
Step-by-step explanation:
(a)A population grows exponentially if it increases by a common ratio(called the growth ratio). We can see from the given information that the population of E.coli doubles every 20 minutes, therefore it is an exponential growth with a growth ratio of 2.
(b)The population, P(t) at any time t of an initial population,
with a growth ratio of r over a period k can be modeled using the function:
![P(t)=P_o\cdot r^{t/k}](https://tex.z-dn.net/?f=P%28t%29%3DP_o%5Ccdot%20r%5E%7Bt%2Fk%7D)
In this Case:
=200
Growth rate,r=2
Growth Period,k=20 minutes
Therefore, the equation that models the function is:
, t is in minutes
Answer:
B
Step-by-step explanation:
Reminder: slope-intercept form is y=mx+b where m is the slope and b is the y intercept
There are two points given on the line: (-1, 2) and (1, -4)
First, find the slope
Reminder: slope is y2-y1/x2-x1
Substituting the numbers into the equation gives -4-(-2)/1-(-1) which would make m=-3
Now that the slope is found, we can use slope point form
Reminder: slope point form is y-y1=m(x-x1)
Substituting the numbers would give this equation:
y-2=-3(x-(-1))
Simplifying the equation would give y=-3x-1.
<span><span>64x2-25y2</span> </span>Final result : (8x + 5y) • (8x - 5y) Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y2" was replaced by "y^2". 1 more similar replacement(s).
Step by step solution:<span> Step 1:</span><span> Equation at the end of step 1 :</span><span><span> (64 • (x2)) - 52y2 </span><span> Step 2:</span></span><span> Equation at the end of step 2:</span><span> 26x2 - 52y2 </span><span>Step 3:</span> Trying to factor as a Difference of Squares :
<span> 3.1 </span> Factoring: <span> 64x2-25y2</span>
Theory: A difference of two perfect squares, <span> A2 - B2 </span>can be factored into <span> (A+B) • (A-B)
</span>Proof :<span> (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 <span>- AB + AB </span>- B2 =
<span> A2 - B2</span>
</span>Note:<span> <span>AB = BA </span></span>is the commutative property of multiplication.
Note:<span><span> AB + AB </span></span>equals zero and is therefore eliminated from the expression.
Check: 64 is the square of 8
Check: 25 is the square of 5
Check:<span> x2 </span>is the square of <span> x1 </span>
Check:<span> y2 </span>is the square of <span> y1 </span>
Factorization is : (8x + 5y) • (8x - 5y)
Final result : (8x + 5y) • (8x - 5y)<span>
</span>