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3 years ago

13

At an electronics store, the price of a tablet is marked down 15% to $212.50. What was the price of the tablet before the markdo

wn?

2 answers:

Cloud [144]3 years ago

8 0

Answer:

The price of the tablet before the markdown was $\$250$

Step-by-step explanation:

Let

x-----> the price of the tablet before the markdown

we know that

$100\%-15\%=85\%=85/100=0.85$

$0.85x=212.50$ ------> linear equation that represent the situation

Solve for x

Divide by $0.85$ both sides

$0.85x/0.85=212.50/0.85$

$x=\$250$

konstantin123 [22]3 years ago

4 0

<span>The answer would be $244.375</span>

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3 years ago

In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C an

Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

$P(x)=Ca^{x-2000}$

So, the population in 2000,

$P(2000)=Ca^{2000-2000}$

$=Ca^{0}$

$=C$

According to the question,

$P(2000)=1$

$\implies C=1$

(b) Similarly,

The population in 2025,

$P(2025)=Ca^{2025-2000}$

$=Ca^{25}$

$=a^{25}$ (∵ C = 1)

Again according to the question,

$P(2025)=1.2$

$a^{25}=1.2$

Taking ln both sides,

$\ln a^{25}=\ln 1.2$

$25\ln a = \ln 1.2$

$\ln a = \frac{\ln 1.2}{25}\approx 0.00729$

$a=e^{0.00729}=1.00731$

Thus, the function that shows the population in year x,

$P(x)=(1.00731)^{x-2000}$ ...... (1)

The population in 2010,

$P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555$

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

$1.4=(1.00731)^{x-2000}$

$\ln 1.4=(x-2000)\ln 1.00731$

$0.33647 = (x-2000)0.00728$

$0.33647 = 0.00728x-14.56682$

$0.33647 + 14.56682 = 0.00728x$

$14.90329 = 0.00728x$

$\implies x=\frac{14.90329}{0.00728}\approx 2047$

Therefore, the country's population might reach 1.4 billion in 2047.

3 0

3 years ago