Two climate scientists are creating models for global rising sea levels. One scientist proposes a 10-year doubling model, which predicts that the change in sea level, R(t), will grow according to the following function: R(t)=(125)/(256)*(2)^((t)/( 10)) where t is the number of years after 2005 . The other scientist proposes a steady increase model where the change in sea level will increase by 5 centimeters (cm) per year. Both models predict that in the year 2105 , the sea level will increase by 500cm. To the nearest centimeter, how much greater is the predictions of the steady increase model than the 10 -year doubling model for the change in sea level in the year 2055 ?

Question

Two climate scientists are creating models for global rising sea levels. One scientist proposes a 10-year doubling model, which predicts that the change in sea level,  R(t), will grow according to the following function:  R(t)=(125)/(256)*(2)^((t)/( 10)) where  t is the number of years after 2005 . The other scientist proposes a steady increase model where the change in sea level will increase by 5 centimeters  (cm) per year. Both models predict that in the year 2105 , the sea level will increase by  500cm. To the nearest centimeter, how much greater is the predictions of the steady increase model than the 10 -year doubling model for the change in sea level in the year 2055 ?

Bytelearn · Accepted Answer

Calculate predicted change in sea level: First, let's calculate the predicted change in sea level for the year 2055 using the 10-year doubling model. We need to find R(t) for t = 2055 - 2005 = 50 years. R(t) = (125/256) * (2)^(t/10)Substitute t = 50 into the equation: Substitute t = 50 into the equation to find R(50). R(50) = (125/256) * (2)^(50/10) R(50) = (125/256) * (2)^5 R(50) = (125/256) * 32Perform multiplication to find R(50): Now, perform the multiplication to find the value of R(50). R(50) = (125/256) * 32 R(50) = 125 * (32/256) R(50) = 125 * (1/8) R(50) = 125/8 R(50) = 15.625 cmCalculate predicted change using steady increase model: Next, calculate the predicted change in sea level for the year 2055 using the steady increase model. The steady increase model predicts a 5 cm increase per year. Since 2055 is 50 years after 2005, the total increase would be 50 years * 5 cm/year.Perform multiplication to find total increase: Perform the multiplication to find the total increase for the steady increase model. Total increase = 50 years * 5 cm/year Total increase = 250 cmFind difference between models for 2055: Now, we need to find the difference between the steady increase model and the 10-year doubling model for the year 2055. Difference = Total increase (steady model) - R(50) (10-year doubling model) Difference = 250 cm - 15.625 cmSubtract values to find the difference: Subtract the values to find the difference. Difference = 250 cm - 15.625 cm Difference = 234.375 cmRound the difference to nearest centimeter: Round the difference to the nearest centimeter. Difference ≈ 234 cm

Full solution

More problems from Solve a system of equations using substitution: word problems

Related topics