Question

Write N as a discrete exponential function of t of the form N(t)=A(1+r)t. (HINT: You will need to find (1+r), where r is the rate. Use N(11)=130 and the initial value N(0)=84 to find it.)

Answer 1

Answer:

$N(t)=84(1+0.0405)^t$.

Step-by-step explanation:

We have been given that $N(11)=130$ and $N(0)=84$. We are asked to write N as a discrete exponential function of t of the form $N(t)=A(1+r)^t$.

Using our given information, we can set an equation as:

$N(0)=A(1+r)^0$

$84=A*1$

$84=A$

Using our given information, we will get:

$N(11)=A(1+r)^{11}$

Substitute the given values:

$130=84(1+r)^{11}$

$\frac{130}{84}=\frac{84(1+r)^{11}}{84}$

$1.5476190476190476=(1+r)^{11}$

Switch sides:

$(1+r)^{11}=1.5476190476190476$

Take 11th root of both sides:

$\sqrt[11]{(1+r)^{11}}=\sqrt[11]{1.5476190476190476}$

$1+r=1.04050024747304$

$r=1.04050024747304-1$

$r=0.04050024747304$

$r\approx 0.0405$

Therefore, our required function would be $N(t)=84(1+0.0405)^t$.