All categories

4 years ago

If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?

1 answer:

6 0

Exponential functions are in the form $f(x)=a*b^x$ , where a is the initial value, b is the growth rate (percent increase) + 1, and x is the number of time periods. Our initial value is 100, and we're given the growth rate + 1 (tripling is the same as increasing by 200%; 200%=2.0; 2.0+1=3). Therefore our function is $p(t)=100*3^t$ .

You might be interested in

What is 18 and 2 tenths as a decimal ?

Fantom [35]

18 tenths is "1.8" and 2 tenths is "0.2" does this answer your question?

6 0

3 years ago

Read 2 more answers

What is the area of this trapezoid?

Lunna [17]

Answer:

D. 192 in²

Step-by-step explanation:

6 0

3 years ago

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .

5 0

4 years ago

ben has agreed to play fewer video games and spend more time studying. he has agreed to play less than 10 hours of video games e

crimeas [40]

You just add 5 1/2 three times, so that would be 5 1/2x3, and then you add that together, which gives you your answer, 16 1/2.

7 0

3 years ago

For each of the equations below, solve for y in terms of x. ! a. 2x – 3y = 12

ira [324]

Answer:

$\large\boxed{y=\dfrac{2}{3}x-4}$

Step-by-step explanation:

$2x-3y=12\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\2x-2x-3y=12-2x\\\\-3y=12-2x\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3y}{-3}=\dfrac{12}{-3}+\dfrac{-2x}{-3}\\\\y=-4+\dfrac{2}{3}x$

7 0

3 years ago