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3 years ago

Find the coordinates of the points of intersection of the graphs with coordinate axes: y=−1.5x+3

Mathematics

1 answer:

mart [117]3 years ago

4 0

Answer:

(0, 3 ) and (2, 0 )

Step-by-step explanation:

To find the y- intercept let x = 0 in the equation and solve for y

y = - 1.5(0) + 3

y = 3 ← y- intercept ⇒ (0, 3 )

To find the x- intercept let y = 0 in the equation and solve for x

0 = - 1.5x + 3 ( subtract 3 from both sides )

- 3 = - 1.5x ( divide both sides by - 1.5 )

x = 2 ← x- intercept ⇒ (2, 0 )

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vivado [14]

Using an exponential function, it is found that the Tequesta settlement is 1845 years old.

<h3>What is an exponential function?</h3>

The exponential equation for a decaying amount of a substance is given by:

$A(t) = A(0)e^{-rt}$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.

$A(t) = A(0)e^{-rt}$

$0.5A(0) = A(0)e^{-5730r}$

$e^{-5730r} = 0.5$

$\ln{e^{-5730r}} = \ln{0.5}$

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$r = -\frac{\ln{0.5}}{5730}$

$r = 0.00012096809$

Hence, the equation is:

$A(t) = A(0)e^{-0.00012096809t}$

The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).

$A(t) = A(0)e^{-0.00012096809t}$

$0.8A(0) = A(0)e^{-0.00012096809t}$

$e^{-0.00012096809t} = 0.8$

$\ln{e^{-0.00012096809t}} = \ln{0.8}$

$-0.00012096809t = \ln{0.8}$

$t = -\frac{\ln{0.8}}{0.00012096809}$

$t = 1845$

The Tequesta settlement is 1845 years old.

You can learn more about exponential functions at brainly.com/question/25537936

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2 years ago

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ankoles [38]

This is how you would write the statement:
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You could also write it like this, if the one-half applies to everything:
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