Math Problem Statement
write the exponential function in the form y = ae^kt. Find k accurate to four decimal places. If t is measured in years, give the percent annual growth rate and the continuous percent growth rate per year. y=4000(0.51)^t
Solution
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Logarithms
Growth and Decay
Formulas
Exponential form: y = ae^{kt}
Natural logarithm: ln(x)
Annual growth rate: (base - 1) * 100
Continuous growth rate: k * 100
Theorems
Properties of Logarithms
Exponential Growth and Decay Theorem
Suitable Grade Level
Grades 10-12