In the U.S. during the first decade of the 2000s, live births to unmarried mothers, B(t), grew accordingly to the exponential model B(t)= 1.307×10^(6) × (1.033)^(t), where t is the number of years after 2000.
What does the model predict for the number of live births to unwed mothers in 2015 and 2020.
*round coefficient to two decimal places *
2015: the model predicts N×10^(n) live births, where N=___ and n=___
2020: the model predicts N×10^(n) live births, where N=___ and n=___
To find the number of live births to unwed mothers in 2015 and 2020 using the given exponential model, we need to substitute the values of t into the equation and calculate the result.
For 2015, t = 2015 - 2000 = 15 years after 2000. Plugging this into the equation:
B(15) = 1.307 × 10^6 × (1.033)^15
Calculating the result, we find that B(15) ≈ 1.307 × 10^6 × 1.608.
Thus, for 2015, the model predicts N × 10^n live births, where N ≈ 1.33 and n ≈ 6.
For 2020, t = 2020 - 2000 = 20 years after 2000. Plugging this into the equation:
B(20) = 1.307 × 10^6 × (1.033)^20
Calculating the result, we find that B(20) ≈ 1.307 × 10^6 × 1.703.
Thus, for 2020, the model predicts N × 10^n live births, where N ≈ 1.37 and n ≈ 6.
Therefore, the predictions are as follows:
2015: The model predicts approximately 1.33 × 10^6 live births.
2020: The model predicts approximately 1.37 × 10^6 live births.