Identify the initial amount ( a…

Maths Questions

Identify the initial amount ( a ) and the growth rate ( r ) (as a percentage) of the exponential function ( y = 350(1 + 0.75)^t ). Evaluate the function when ( t = 5 ) and round your answer to the nearest tenth.

Answer

A. Initial amount ( a = 350 ) and growth rate ( r = 75% ). B. 5744.6. Step-by-step explanation: The exponential function given is ( y = 350(1 + 0.75)^t ). A. An exponential function is formulated as ( y = a cdot b^x ), where ( a ) represents the initial value and ( b ) indicates growth, expressed as ( (1 + r) ) with ( r ) in decimal. Thus, the structure is ( y = a cdot (1 + r)^x ). By comparing this to our function, we identify that ( a = 350 ) and ( r = 0.75 ). To convert the decimal growth rate into a percentage, we multiply by 100: ( r = 0.75 times 100 = 75% ). Hence, the initial amount is ( 350 ) and the growth rate is ( 75% ). B. Now, let’s calculate the function at ( t = 5 ) by substituting ( t = 5 ) into the equation: ( y = 350(1 + 0.75)^5 ), leading to ( y = 350(1.75)^5 ), further simplifying to ( y = 350 times 16.4130859375 ) which results in ( y approx 5744.6 ). Thus, at ( t = 5 ), we find ( 5744.6 ).

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