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2 years ago

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The general form for a compound interest function is B(t)=P(1+r/n)^nt . Assuming that n=1 , rewrite the compound interest equati

on B(t)=900(1.185)^t in the general form. Using your rewritten equation, what is the percent rate of change?

1 answer:

Vesnalui [34]2 years ago

3 0

The formula $B(t)=P(1+\frac{r}{n})^{nt}$ , for n=1 becomes $B(t)=P(1+\frac{r}{1})^{1\cdot t}=P(1+r)^t$ .

Comparing $B(t)=P(1+r)^t$ with $B(t)=900(1.185)^t$ , we see that

P=900, and 1+r=1.185, which means that r=0.185.

r=0.185 can be written as 18.5%, as a percentage.

Answer: 18.5%

You might be interested in

Alex

Answer:

The correct option is C ) 109.5°

Therefore,

$m\angle E=109.5\°$

Step-by-step explanation:

Given:

In Triangle DEF

d = 10

e = 18

f = 12

To Find

angle E = ?

Solution:

In Triangle DEF , Cosine Rule says

$\cos E=\dfrac{f^{2}+d^{2}-e^{2}}{2fd}$

Substituting the values we get

$\cos E=\dfrac{12^{2}+10^{2}-18^{2}}{2\times 12\times 10}$

$\cos E=\dfrac{-80}{240}=-\dfrac{1}{3}$

Therefore,

$\angle E=\cos^{-1}(-0.3333)$

$m\angle E=109.5\°$ ............As it is in Second Quadrant

Therefore,

$m\angle E=109.5\°$

4 0

3 years ago

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

2 years ago

If you horizontally compress exponential function f(x)=2^x by a factor by a of 5, which of these is the equation of the new func

Zolol [24]

The anwser is -2x my dude

8 0

3 years ago

Read 2 more answers

Find the area of the triangle below.<br>Be sure to include the correct unit in your answer.<br><br>

OleMash [197]

Answer:

area of triangle= 1/2*h*b

= 1/2*6*16

=3*16

= 48 yd²

This is your answer. If I'm right so,

Please mark me as brainliest. thanks!!!

5 0

2 years ago

Chin canned a number of quart jars anf a number of pints jars of tomatoes from hid garden. A pint is 16 onces and a quart is 32

ryzh [129]

Answer:

The equation which models the scenario is: 16 p + 32 q = 1280

Step-by-step explanation:

The total number of pints packed = p

The total number of quarts packed = q

The weight of 1 pint jar of tomatoes = 16 oz

So, the total weight of p pints = p x ( Weight of 1 pint) = p x ( 16 oz) = 16 p

The weight of 1 quart jar of tomatoes = 32 oz

So, the total weight of q quarts = q x ( Weight of 1 quart) = q x ( 32 oz)

= 32 q

Now, the TOTAL WEIGHT of p pints and q quarts

= Total weight of { p pints + q quarts} = 16 p + 32 q

Also, chin canned a total of 1280 ounces.

⇒ TOTAL WEIGHT of p pints and q quarts = 1280 ounces

or, 16 p + 32 q = 1280 ounces

Hence, equation which models the scenario is: 16 p + 32 q = 1280

8 0

3 years ago