To determine: C and a so that $f\left(x\right)=C{a}^{x}$ satisfies given conditions.

Given:$f\left(0\right)=3;f\left(3\right)=24$

Given:

Tazmin Horton
2021-09-24
Answered

To determine: C and a so that $f\left(x\right)=C{a}^{x}$ satisfies given conditions.

Given:$f\left(0\right)=3;f\left(3\right)=24$

Given:

You can still ask an expert for help

StrycharzT

Answered 2021-09-25
Author has **102** answers

Formula used:

If$b}^{x}={a}^{x$ with $a,b>0$ then $b=a$ .

Calculation:

Consider the given function$f\left(x\right)=C{a}^{x}$ . Substituting $x=0$ we get

This gives,$C=3$ .

Substituting$x=3\in f\left(x\right)=3{a}^{x}$ we get

$f\left(3\right)=24=3{a}^{3}$

$a}^{3}=\frac{24}{3$

$a}^{3}=8={2}^{3$

This gives$a=3$ .

Conclusion:

From the given conditions we find$f\left(x\right)=3\left({2}^{x}\right)$

If

Calculation:

Consider the given function

This gives,

Substituting

This gives

Conclusion:

From the given conditions we find

asked 2021-09-17

The function $y=3.5x+2.8$ represents the cost y (in dollars) of a taxi ride of x miles.

a. Identify the independent and dependent variables.

b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

a. Identify the independent and dependent variables.

b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

asked 2021-09-07

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe.

asked 2021-08-18

To find:

a) The speed of the sprinter while he running as crossed the finish line

b) After how many seconds was he running at the rate of 10 m per sec

Using the model function$f\left(t\right)=11.65(1-{e}^{-\frac{t}{1.27}})$ where f(t) is the speed of the sprinter per second after t seconds.

a) The speed of the sprinter while he running as crossed the finish line

b) After how many seconds was he running at the rate of 10 m per sec

Using the model function

asked 2021-09-22

The expression $\frac{\sqrt{7}}{\sqrt{28}}$

asked 2021-09-07

The solution of equation $\mathrm{log}(2-x)=0.5$

asked 2021-09-18

An expression for f(x) and g(x):

asked 2021-09-11

Choose one technology and explain why it is useful for modeling complex systems.