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4 years ago

The graph of an exponential function of the form y = f(x) = a^x passes through the points and . The graph lies the x-axis.

1 answer:

7 0

$y=f(x)=a^x,\ a\in\mathbb{R^+}\ \wedge\ a\neq1\\\\f(0)=a^0=1\to\ \text{BLANK A}\ (0,\ 1)\\\\f(1)=a^1=a\to\text{BLANK B}\ (1,\ a)\\\\\text{BLANK C}\ above\\\text{because for each positive number its power is a positive number}$

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The breakdown of a sample of a chemical compound is represented by the function p(t) = 500 (0.25)^t, where p(t) represents the n

ludmilkaskok [199]

Given:

The function is:

$p(t)=500(0.25)^t$

Where p(t) represents the number of milligrams of the substance and t represents the time.

To find:

The correct explanation for the number 0.25 and 500 in the given function.

Solution:

The general exponential function is:

$y=ab^x$ ...(i)

Where, a is the initial value and b is the growth/decay factor. If $0$ , then decay factor and if $b>1$ , then growth factor.

We have,

$p(t)=500(0.25)^t$ ...(ii)

On comparing (i) and (ii), we get

$a=500$ , it means initial there are 500 milligrams of the substance.

$b=0.25$ , this value is less than 1, it means the substance is decreasing by a factor of 0.25.

Therefore, 0.25 means the substance is decreasing by a factor of 0.25 and 500 means the initial value of substance is 500 milligram.

3 0

3 years ago

Suppose a new car is worth $30,000. You can use the function y=30,000(0.85)^x to estimate the car’s value after x years. What is

ANEK [815]

The decay factor here is 0.85, and it means the car’s value changes by 85% every year, or goes down by 15% every year.

The formula for exponential decay is y = a(1 - b)^x

y is the final amount.

a is the initial amount, which is $30,000 in this case.

(1 - b) is the decay factor, or the number the original value gets multiplied by each year, which is 0.85 here.

b is the percent decrease in decimal form. In this case, we can find it using the formula (1 - b) = 0.85. We soon find that b = 0.15, or 15%.

x is the number of years.

5 0

3 years ago

Please help me out with this

Sergio039 [100]

Answer:

Step-by-step explanation:

4(10)-2(10+-3)

40-2(7)

40-14

8 0

3 years ago

Read 2 more answers

Find a formula for the exponential function passing through the points (-1,5/3) and (3, 135).

Artyom0805 [142]

The expression y = 4.998 · $e^{1.098\cdot x}$ is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).

<h3>How to derive an exponential function that passes through two given points</h3>

Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:

$y = A \cdot e^{B \cdot x}$

Where:

A - y-Intercept of the exponential function.
B - Growth factor
x - Independent variable.
y - Dependent variable.

Which is equivalent to the following logarithmic expression:

㏑ y = ㏑ A + B · x

If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:

㏑ (5 / 3) = ㏑ A - B

㏑ 135 = ln A + 3 · B

Then, we solve the system by numerical methods:

㏑ A = 1.609 (A = 4.998), B = 1.098

And the exponential function is equal to y = 4.998 · $e^{1.098\cdot x}$ .

To learn more on exponential functions: brainly.com/question/11487261

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6 0

2 years ago

an investment is expected to pay 5 per year compounded continuously. If you want the value of the investment to be $700,000 afte

andre [41]

The multiplier for continuous compounding is e^(rt). You want
700,000 = P·e^(0.05·25) ≈ 3.490343P
Then
700,000/3.490343 = P

You should invest $200,553 initially.

8 0

4 years ago