The town of Valley View conducted a census this year, which showed that it has a population of 1,800 people. Based on the census data, it is estimated that the population of Valley View will grow by 12% each decade. Write an exponential equation in the form y = a(b)^x that can model the town population, y, x decades after this census was taken. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = ______

Question

The town of Valley View conducted a census this year, which showed that it has a population of 1,800 people. Based on the census data, it is estimated that the population of Valley View will grow by 12% each decade. Write an exponential equation in the form y = a(b)^x that can model the town population, y, x decades after this census was taken. Use whole numbers, decimals, or simplified fractions for the values of a and b.   y = ______

Bytelearn · Accepted Answer

Convert to decimal: Convert the percentage growth rate to a decimal. To convert a percentage to a decimal, divide by 100. r = 12% = 12 / 100 = 0.12Calculate growth factor: Determine the growth factor (b). For exponential growth, the growth factor b is calculated by adding 1 to the growth rate expressed as a decimal. Growth factor: b = 1 + rCalculate value of growth factor: Calculate the value of the growth factor (b). Substitute r = 0.12 into the formula b = 1 + r. b = 1 + 0.12 b = 1.12Identify initial population and growth factor: Identify the initial population (a) and the growth factor (b) to write the exponential equation. The initial population (a) is given as 1800. The growth factor (b) we calculated is 1.12. The exponential equation in the form y = a(b)^x is: y = 1800(1.12)^x

Full solution

More problems from Write exponential functions: word problems

Related topics