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4 years ago

The function f(x)=5(2)^x was replaced with f(x)+k , resulting in the function graphed below. what is the value of k?

Mathematics

1 answer:

xxTIMURxx [149]4 years ago

5 0

Since adding a constant to a function simply moved the graph upwards by that amount, solve f(x) for any value and see how much the graph given is different from that value of y...the simplest way in this case may be to simply find f(0) which is:

5*2^0=5

Clearly the graph at x=0 is at y=-2 so we can see that k is:

5+k=-2 so

k=-7

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3 years ago

3. At the start of summer, Ben has $250 . He takes a summer

earnstyle [38]

Answer:

Week 4

Step-by-step explanation:

Ben has $250 in the beginning. He saves $150 per week.

y = 150x + 250

Tim has $1,650 in the beginning. He spends $200 per week.

y = 1650 - 200x

We are trying to find which x-value produces the same y-value for both equations. You can do this by setting both equations equal to each other.

150x + 250 = 1650 - 200x

(150x + 250) + 200x = (1650 - 200x) + 200x

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3 years ago

What is the exact time t, in years, needed for the balance of an account that earns 5% annual 8. Interest compounded continuousl

Brums [2.3K]

Answer:

It takes 22.52 years for the balance to triple in value.

Step-by-step explanation:

Continuous compounding:

The amount of money earned using continuous compounding is given by the following equation:

$A(t) = A(0)(1+r)^t$

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.

Interest rate of 5%.

This means that $r = 0.05$ , and thus:

$A(t) = A(0)(1+r)^t$

$A(t) = A(0)(1+0.05)^t$

$A(t) = A(0)(1.05)^t$

Time for the balance to triple?

This is t for which $A(t) = 3A(0)$ . So

$A(t) = A(0)(1.05)^t$

$3A(0) = A(0)(1.05)^t$

$(1.05)^t = 3$

$\log{(1.05)^t} = \log{3}$

$t\log{1.05} = \log{3}$

$t = \frac{\log{3}}{\log{1.05}}$

$t = 22.52$

It takes 22.52 years for the balance to triple in value.

3 0

3 years ago

Rectangle QRST is dilated with the origin as the center of dilation to create rectangle Q'R'S'T'.

scoundrel [369]

Answer:

Rule: dilation about the origin by a scale factor of 2

Step-by-step explanation:

Given

See attachment for QRST and Q'R'S'T

Required

The dilation rule

First, we calculate the scale factor (k)

From the attachment, we have:

$QR = 4$

$Q'R' = 8$

k, is then calculated as:

$k = \frac{Q'R'}{QR}$

$k = \frac{8}{4}$

$k =2$

<em>Hence, QRST is dilated by a factor of 2</em>

3 0

3 years ago

Use the graphing calculator to graph these functions: y1= 2x ; y2= 2x2 ; y3 = 2x After what y-value does the exponential functio

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After the value of y is 4 does the exponential function definitely surpasses the linear function.

What is exponential function?

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

Given

Use the graphing calculator to graph these functions: y1= 2x ; y2= 2x2 ; y3 = 2x.

As we can see y1=2x is a linear function and y3=2^x is a exponential function.

The graphs of y1 and y3 meet at 2 points i.e. at (1,2) and (2,4)

When you graph the equations their point of intersection is (2,4).

Therefore, when y > 4, the exponential function surpasses the linear function.

To know more about linear function click the link given below.

brainly.com/question/6714976

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2 years ago