Question

How to find exponential function?

Answer 1

To find an exponential function, identify the base and exponent. The general form is y = a * b^x, where 'a' is the initial value, 'b' is the base, and 'x' is the exponent.

Step-by-step explanation:

To find an exponential function, we need to identify the base and the exponent. The general form of an exponential function is y = a * b^x, where 'a' is the initial value, 'b' is the base, and 'x' is the exponent. For example, the exponential function y = 2^x represents exponential growth with a base of 2. It means that each time 'x' increases by 1, the value of 'y' doubles.

Answer 2

`\huge\mathbb{ \underline{SOLUTION :}}`

Given:

• 
  `\bold{y=Ce^(kt)}`

• 
  `\bold{(5,5)}`

• 
  `\bold{(0, (6)/(7) )}`

`\small\leadsto\bold{Substitute:}`

`\longrightarrow\sf{ (6)/(7)= Ce^(k*0)}`

`\longrightarrow\sf{(6)/(7)= C*e^0}`

`\longrightarrow\sf{e^0=1}`

`\therefore\sf{C= (6)/(7) }`

`\therefore\sf{5=Ce^(k*5)}`

`\\`

`\bold{Solve \: to \: find \: k:}`

`\longrightarrow\sf{5 = (6)/(7) *e^(k5)}`

`\longrightarrow\sf{ (7*5)/(6) *e^(5k)}`

`\longrightarrow\sf{In=( (35)/(6) ) = 5k}`

`\longrightarrow\sf{1.76=5k}`

`\longrightarrow\sf{k=(1.76)/(5) = 0.352}`

`\huge \mathbb{ \underline{ANSWER:}}`

`\large\sf{\boxed{\sf (6)/(7)= e^(0.352*t)}}`