help please on math algebra 2

Question

_{The number of views on a viral video can be modeled by the function S(t)=20(1.141)4 to the T exponent. Write an equivalent function of the form} 

 _{Round your final values to 4 decimal places.}

Answer 1

S(t) = 20·(1.141)^4t

You can write any exponential equation with a different base using the "Change of Base" formula:

a^x = b^x·logb(a)

Where we changed from base a to base b and logb is log base b. So you can re-write your equation with a base of 10 using log base 10 (written as just log):

S(t) = 20·(1.141)^4t

S(t) = 20·10^{4t·log(1.141)} ≈ 20·10^0.229t

Where log(1.141) ≈ 0.057 according to my calculator. You could also change to a base of e (using log base e written as ln):

S(t) = 20·e^{4t·ln(1.141)} ≈ 20·e^0.528t

where ln(1.141) ≈ 0.132.