how do you do 27?????

Hey there!

To start, the equation needed to represent this problem would be an equation:
y= ab^x

a represents the initial amount. In this case, the initial amount would be 4 billion. It would be represented as 4 since each 1= one billion.

b represents the rate. Because the problem discusses a growth, convert the rate, 1.9% to a decimal and add 1 to it (add one if it is a growth, subtract one if it is a decay). b would be 1.019.

x represents the time in which the population grows or t.

When you piece this together, your equation should look like:
y=4(1.019)^t

or

Choice A.

Hope this helps and have a nice day! Feel free to ask any questions about my work. :)

JonHenderson55 JonHenderson55 · Answer 2 · 2018-05-05T22:20:59+02:00

The correct answer is: [A]: " P(t) = 4 * (1 .019)^t " .
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Explanation:
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Use the formula for "exponential growth" :
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→ " y = A * (1 + r)^t " ;
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in which:
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A = the "beginning population" ;

→ (in number representing "billions of people") ;

→ given the "beginning population" is "4 billion" ;

→ " A = 4 " ;
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r = rate (of change) = 1.9% ; expressed as a decimal:

→ "r = rate = 1.9% = { 1.9 ÷ 100 } ;

→ {Take the "1.9" ; & move the decimal point 2 (two) spaces backward }:

→ 1.9% = 1.9 ÷ 100 = 0.019 ;

→ " r = 0.019 " ;

→ " t = time" ; (usually in "years" ; however, all the answer choices provided leave the "t" as it is; so we shall do so, too.
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→ Replace "y" with: " P(t) " ;

→ And rewrite the equation of the function with our known values:

→ " y = A * (1 + r)^t " ;
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→ becomes:

→ " P(t) = 4* (1 + 0.019)^t " ;

→ " P(t) = 4 * (1 .019)^t " ;
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→ which is: Answer choice: [A]: " P(t) = 4 * (1 .019)^t " .
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