Question 1197628




Part 1

Express the answer in terms of a natural logarithm.

Exponential expressions with natural base e are of the form {{{y = a*e^(kx)}}}. The value of 'a' is already set to be 3.4 since this is the coefficient of the given equation. We just need to find k



So set {{{(0.4)^x}}} equal to {{{e^(kx)}}} and solve for k

{{{(4.8)^x = e^(kx)}}}

{{{(4.8)^x = (e^k)^x}}}

{{{4.8 = e^k}}} The two sides have the same exponent of x. So the two bases are 4.8 and {{{e^k}}} must be equal.

{{{ln(4.8) = k}}} Convert to logarithmic form

{{{k = ln(4.8)}}}


{{{y = 101*e^(ln(4.8)x)}}}



Part 2:

Simplify the​ answer, rounding to three decimal places.

{{{y = 101*e^(ln(4.8)x)}}}..............{{{ln(4.8)=1.5686159179138452=1.569}}}

{{{y = 101*e^(1.569x)}}}