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3 years ago

What is the value of x? Enter your answer in the box.

Mathematics

1 answer:

Andrews [41]3 years ago

5 0

Answer:

$\displaystyle 7 = x$

Step-by-step explanation:

Five is <em>one-eighth</em> of forty, so relatively proportional to that, <em>one-eighth</em> of twenty-four is three, so you do this:

24 = 2x + 10

- 10 - 10

__________

$\displaystyle \frac{14}{2} = \frac{2x}{2} \\ \\ 7 = x$

I am joyous to assist you anytime.

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3 years ago

A countrys population in 1990 was 145 million. In 1998 it was 151 million. Estimate the population in 2015 using the exponential

alexandr402 [8]

Answer:

The population in 2015 will be 165 million.

Step-by-step explanation:

The exponential growth formula is given by:

$f(t) = a(1 + r)^{\Delta t}$

Where:

a: is the initial population

r: is the rate of increase

Δt: is the time

With the initial information we can find the rate:

$151 = 145(1 + r)^{1998-1990}$

Using logarithm:

$ln(151) = ln(145) + 8[ln(1 + r)]$

$ln(1 + r) = \frac{ln(151) - ln(145)}{8}$

$ln(1 + r) = 5.0683 \cdot 10^{-3}$

Using exponential:

$e^{ln(1 + r)} = e^{5.0683 \cdot 10^{-3}}$

$r = 5.081 \cdot 10^{-3}$

Now, we can find the estimated population in 2015:

$f(t) = 151(1 + 5.081 \cdot 10^{-3})^{2015-1998}$

$f(t) = 165$

Therefore, the population in 2015 will be 165 million.

I hope it helps you!

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