From 1945 to 2008 , one country's per capita gross domestic product (GDPPC) increased about 6% per year, ending at $19,600. For the next few years, the growth slowed to an increase of about $1,300 per year. To the nearest dollar, how much less did the GDPPC grow during the next 6 years than it would have if it had maintained its earlier growth rate? ◻

Question

From 1945 to 2008 , one country's per capita gross domestic product (GDPPC) increased about  6% per year, ending at  $19,600. For the next few years, the growth slowed to an increase of about  $1,300 per year. To the nearest dollar, how much less did the GDPPC grow during the next 6 years than it would have if it had maintained its earlier growth rate?  ◻

Bytelearn · Accepted Answer

Calculate GDPPC Growth: First, we need to calculate the GDPPC growth over the next 6 years if it had maintained the 6% per year growth rate. The formula for compound growth is: GDPPC_end = GDPPC_start * (1 + growth_rate)^number_of_years Here, GDPPC_start is $19,600, growth_rate is 6% or 0.06, and number_of_years is 6.Perform Calculation: Now, we perform the calculation: GDPPC_end = $19,600 * (1 + 0.06)^6 Using a calculator, we find: GDPPC_end ≈ $19,600 * (1.418519) GDPPC_end ≈ $27,803.17 This is the GDPPC at the end of 6 years with a 6% growth rate per year.Calculate Slower Growth: Next, we calculate the GDPPC growth with the slower rate of $1,300 per year for 6 years. The formula for linear growth is: GDPPC_end = GDPPC_start + (increase_per_year * number_of_years) Here, GDPPC_start is $19,600, increase_per_year is $1,300, and number_of_years is 6.Find Difference: Now, we perform the calculation: GDPPC_end = $19,600 + ($1,300 * 6) GDPPC_end = $19,600 + $7,800 GDPPC_end = $27,400 This is the GDPPC at the end of 6 years with a growth of $1,300 per year.Perform Subtraction: Finally, we find the difference between the GDPPC growth at the 6% rate and the slower $1,300 per year rate. Difference = GDPPC_end (6% growth) - GDPPC_end ($1,300/year growth) Difference = $27,803.17 - $27,400Now, we perform the subtraction: Difference ≈ $403.17 To the nearest dollar, the GDPPC grew $403 less during the next 6 years than it would have if it had maintained its earlier growth rate of 6% per year.

Full solution

More problems from Percent of change: word problems

Related topics