Write an exponential function to model the following situation.

Mathematics

1 answer:

valentinak56 [21]3 years ago

3 0

Answer:

y = 130,000(1.03)ˣ

Step-by-step explanation:

The general form of an exponetial function is y = abˣ, where a is the initial value (when x = 0), and b is the multiplier (the growth or decay factor). Here, we start with a population of 130,000, so our initial value a = 130,000. A growth of 3% each year represents a growth factor of 1.03, so after x years, the population y should be y = 130,000(1.03)ˣ.

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If point P is 4/7 of the distnace frm M to N, what ratio does the point P partiion the directed line segment from M to N

vredina [299]

Answer: 4:3.

Step-by-step explanation:

Given: Point P is $\dfrac{4}{7}$ of the distance from M to N.

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If Point P is between points M and N, then the ratio can be written as

$\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}$

As per given,

$\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}$