SAT Question dd8ac009: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. It's given that the relationship between $t$ and $d$ is exponential. The table shows that the value of $d$ increases as the value of $t$ increases. Therefore, the relationship between $t$ and $d$ can be represented by an increasing exponential equation of the form $d=a{\left(1+b\right)}^t$, where $a$ and $b$ are positive constants. The table shows that when $t=0$, $d=670$. Substituting $0$ for $t$ and $670$ for $d$ in the equation $d=a{\left(1+b\right)}^t$ yields $670=a{\left(1+b\right)}^0$, which is equivalent to $670=a\left(1\right)$, or $670=a$. Substituting $670$ for $a$ in the equation $d=a{\left(1+b\right)}^t$ yields $d=670{\left(1+b\right)}^t$. The table also shows that when $t=1$, $d=674.02$. Substituting $1$ for $t$ and $674.02$ for $d$ in the equation $d=670{\left(1+b\right)}^t$ yields $674.02=670{\left(1+b\right)}^1$, or $674.02=670\left(1+b\right)$. Dividing both sides of this equation by $670$ yields $1.006=1+b$. Subtracting $1$ from both sides of this equation yields $b=0.006$. Substituting $0.006$ for $b$ in the equation $d=670{\left(1+b\right)}^t$ yields $d=670{\left(1+0.006\right)}^t$. Therefore, of the choices, choice B best represents the relationship between $t$ and $d$.